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The area of triangle KLM is equal to the area of rectangle

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The area of triangle KLM is equal to the area of rectangle [#permalink] New post 06 Jun 2017, 06:29
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The area of triangle KLM is equal to the area of rectangle ABCD. If the perimeter of ABCD is 16, what is the length of LM ?

A) \frac{3}{2}

B) 3

C) \frac{16}{5}

D) 5

E) 6
[Reveal] Spoiler: OA

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Re: The area of triangle KLM is equal to the area of rectangle [#permalink] New post 06 Jun 2017, 16:14
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Carcass wrote:


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The area of triangle KLM is equal to the area of rectangle ABCD. If the perimeter of ABCD is 16, what is the length of LM ?

A) \frac{3}{2}

B) 3

C) \frac{16}{5}

D) 5

E) 6


The perimeter of ABCD is 16
Let x = length of side BC
This also means x = length of side AD
Also, we can see that CD has length 3
So, we get: x + x + 3 + 3 = 16
Simplify: 2x + 6 = 16
Solve: x = 5
So, side BC has length 5
So, the AREA of rectangle ABCD = (5)(3) = 15

The area of triangle KLM is equal to the area of rectangle ABCD.
We know the area of rectangle ABCD = 15
So, the area of triangle KLM = 15

Area of triangle = (base)(height)/2
Substitute to get: 15 = (side LM)(5)/2
Multiply both sides by 2 to get: 30 = (side LM)(5)
Divide both sides by 5 to get: 6 = side LM

Answer:
[Reveal] Spoiler:
E


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Re: The area of triangle KLM is equal to the area of rectangle   [#permalink] 06 Jun 2017, 16:14
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