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505-555 (Easy)|   Geometry|      
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The area of triangle KLM is equal to the area of rectangle ABCD. If th 13 Jun 2018, 12:23
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E
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86% (01:12) correct 14% (01:14) wrong based on 85 sessions

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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


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E
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The area of triangle KLM is equal to the area of rectangle ABCD. If th 13 Jun 2018, 14:15
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Perimeter of ABCD = 2(3+AD) =16
AD =5
Area of ABCD =5*3 =15
Area of triangle KLM =1/2(5)(LM)
15 = 1/2(5)(LM)
LM=6
Option E
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The area of triangle KLM is equal to the area of rectangle ABCD. If th 13 Jun 2018, 14:22
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E
Rectangle is 3 by 5
Area is 15
15 = LM * 5/2
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The area of triangle KLM is equal to the area of rectangle ABCD. If th 13 Jun 2018, 22:16
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Solution



Given:
    • The area of triangle KLM is equal to the area of rectangle ABCD
    • Perimeter of ABCD is 16

To find:
    • The length of LM

Approach and Working:
If we assume the length of rectangle is x, then we can write
    • 2 (x + 3) = 16
    Or, x + 3 = 8
    Or, x = 5

Therefore, the area of the rectangle ABCD = 5 * 3 = 15 = the area of triangle KLM

Also, the area of triangle KLM can be written as
    • ½ * LM * 5 = 15
    Or, LM = 6

Hence, the correct answer is option E.

Answer: E
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The area of triangle KLM is equal to the area of rectangle ABCD. If th 14 Jun 2018, 08:10
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Bunuel

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


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Given, Area of rectangle=Area of triangle
Or, 3*AD=1/2*LM*5
Or, LM=\(\frac{6}{5}\)*AD----------(1)

Given, perimeter of rectangle=16
Or,2(AB+AD)=16 or, 2AD=16-2*5 Or, AD=5

Hence from(1), we have LM=\(\frac{6}{5}\)*5=6

Ans. (E)
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The area of triangle KLM is equal to the area of rectangle ABCD. If th 17 Jun 2018, 19:44
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Bunuel

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


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We can let LM = n and BC = m and create the equation:

3m = n x 5 x 1/2

6m = 5n

We also know that:

2(3) + 2m = 16

2m = 10

m = 5

Thus,

6 x 5 = 5n

6 = n

Alternate Solution:

Let’s let BC = x. Since the perimeter of ABCD is 16, we know that 3 + 3 + x + x = 16, so x = 5. Thus, we know that the area of rectangle ABCD = area of triangle KLM = 3 x 5 = 15.

We know that the area of a triangle is 1/2 * b * h. Thus, for triangle KLM, we have:

1/2 x LM x 5 = 15

5 x LM = 30

LM = 6

Answer: E
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