Let ABC be a triangle such that AB=13 BC=14 and CA=15. D is a point on BC such that AD Bisects

Answers

Answer 1

Answer:

Area of triangle ADC  is 54 square unit

Step-by-step explanation:

Here is the complete question:

Let ABC be a triangle such that AB=13, BC=14, and CA=15. D is a point on BC such that AD bisects angle A. Find the area of triangle ADC .

Step-by-step explanation:

Please see the attachment below for an illustrative diagram

Considering the diagram,

BC = BD + DC = 14

Let BD be [tex]x[/tex] ; hence, DC will be [tex]14-x[/tex]

and AD be [tex]y[/tex]

To, find the area of triangle ADC

Area of triangle ADC  = [tex]\frac{1}{2} (DC)(AD)[/tex]

= [tex]\frac{1}{2}(14-x)(y)[/tex]

We will have to determine [tex]x[/tex] and [tex]y[/tex]

First we will find the area of triangle ABC

The area of triangle ABC can be determined using the Heron's formula.

Given a triangle with a,b, and c

[tex]Area =\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Where [tex]s = \frac{a+b+c}{2}[/tex]

For the given triangle ABC

Let [tex]a[/tex] = AB, [tex]b[/tex] = BC, and [tex]c[/tex] = CA

Hence, [tex]a = 13, b= 14,[/tex] and [tex]c = 15[/tex]

∴ [tex]s = \frac{13+14+15}{2} \\s= \frac{42}{2}\\s = 21[/tex]

Then,

Area of triangle ABC = [tex]\sqrt{(21)(21-13)(21-14)(21-15)}[/tex]

Area of triangle ABC = [tex]\sqrt{(21)(8)(7)(6)}[/tex] = [tex]\sqrt{7056}[/tex]

Area of triangle ABC = 84 square unit

Now, considering the diagram

Area of triangle ABC = Area of triangle ADB + Area of triangle ADC

Area of triangle ADB = [tex]\frac{1}{2} (BD)(AD)[/tex]

Area of triangle ADB = [tex]\frac{1}{2}(x)(y)[/tex]

Hence,

Area of triangle ABC =  [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]

84 =   [tex]\frac{1}{2}(x)(y)[/tex] + [tex]\frac{1}{2}(14-x)(y)[/tex]

∴ [tex]84 = \frac{1}{2}(xy) + 7y - \frac{1}{2}(xy)[/tex]

[tex]84 = 7y\\y = \frac{84}{7}[/tex]

∴ [tex]y = 12[/tex]

Hence, [tex]y =[/tex] AD = 12

Now, we can find BD

Considering triangle ADB,

From Pythagorean theorem,

/AB/² = /AD/² + /BD/²

∴13² = 12² + /BD/²

/BD/² = 169 - 144

/BD/ = [tex]\sqrt{25}[/tex]

/BD/ = 5

But, BD + DC = 14

Then, DC = 14 - BD = 14 - 5

BD = 9

Now, we can find the area of triangle ADC

Area of triangle ADC  = [tex]\frac{1}{2} (DC)(AD)[/tex]

Area of triangle ADC  = [tex]\frac{1}{2} (9)(12)[/tex]

Area of triangle ADC  = 9 × 6

Area of triangle ADC  = 54 square unit

Hence, Area of triangle ADC  is 54 square unit.

Let ABC Be A Triangle Such That AB=13 BC=14 And CA=15. D Is A Point On BC Such That AD Bisects

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Answer:

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Step-by-step explanation:

A woman making $3000 per month has her salary reduced by 10% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 20% raise over her reduced salary. Find her salary after the raise.

Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

8 is the hundredth place in 737.88, and 8 rounds up. So, the answer is 737.9

Answer:

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Step-by-step explanation:

When we round something to the nearest ___ place, we want to look to the value to the right of it.

Since we're rounding it to the nearest tenths place, we want to look at the value to the right of it - the hundredths place.

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Answers

Answer:

-6

Step-by-step explanation:

When an exponent is outside and inside the parenthesis you need to add them to get rid of the the parenthesis.  The answer is -6 because -6*2 is -12.

Hope this helps. If you have questions put them in the comments.

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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6 dimes in total

6:36

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Answers

Step-by-step explanation:

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Answer:

We place 9 in the first expression instead of h (x)

Then we solve the equation

9=-x-4

x=-13

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

Plz Mark me as brainliest

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

1, 81, and 121 are correct

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answer:

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Answers

Answer:

$140

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{m = 140}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{1.9m + 14 = 2m}[/tex]

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Collect like terms

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Divide both sides by -0.1

[tex] \dashrightarrow{ \sf{ \frac{ - 0.1m} { - 0.1} = \frac{ - 14}{ - 0.1}}} [/tex]

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[tex] \dashrightarrow{ \sf{m = 140}}[/tex]

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Answers

Answer:

7i+20j-31k

Step-by-step explanation:

Given the vectors u (3,5,-8) and v (2,-5,7), they can also be written as;

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To express the vector 3u - v in vector form, first let us find the vector 3u;

3u = 3(3i+5j-8k)

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Subtract v from the resulting vector.

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collect the like terms

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Answers

the reciprocal in decimal is 0.05 as a fraction it could be 5/4

1/25, 1/4 , 0.2 least to greatest

Answers

Answer:

1/25   0.2   1/4

Step-by-step explanation:

1/25, 1/4 , 0.2

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Revenue per occupied room per night $ 75
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b. Write the expression for total revenue per month, first using the general variables, and second including the values of known variables).
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d. What percentage of rooms would need to be occupied, on average, to break even?

Answers

Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Monthly fixed cost= $6,000

Variable cost per occupied room per night= $20

Revenue per occupied room per night= $75

First, we need to structure the total cost formula:

Total cost= 6,000 + 20*x

x= occupied room

Now, we can find the expression for total revenue:

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Revenue= $13,800

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Answers

Answer:

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Step-by-step explanation:

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Answer:

Hey there!

If angle one is congruent to angle two, all of the above is true.

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