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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]  06 Jun 2017, 06:29
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Question Stats:

87% (00:31) correct 12% (01:04) wrong based on 16 sessions

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]  06 Jun 2017, 16:14
Expert's post
Carcass wrote:

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

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

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