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# The length of the diagonal of a certain rectangle is 8. If the sum of

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Math Expert
Joined: 02 Sep 2009
Posts: 49275
The length of the diagonal of a certain rectangle is 8. If the sum of  [#permalink]

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28 Aug 2018, 05:26
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Difficulty:

55% (hard)

Question Stats:

63% (01:31) correct 37% (02:30) wrong based on 49 sessions

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The length of the diagonal of a certain rectangle is 8. If the sum of the lengths of the sides is 10, what is the area of the rectangle?

A. 18
B. 36
C. 64
D. 80
E. It cannot be determined.

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Director
Joined: 20 Feb 2015
Posts: 733
Concentration: Strategy, General Management
Re: The length of the diagonal of a certain rectangle is 8. If the sum of  [#permalink]

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28 Aug 2018, 05:35
Bunuel wrote:
The length of the diagonal of a certain rectangle is 8. If the sum of the lengths of the sides is 10, what is the area of the rectangle?

A. 18
B. 36
C. 64
D. 80
E. It cannot be determined.

a+ b = 10
a^2 + b^2 = 100 -2ab
64 = 100-2ab
2ab = 36 , ab=18
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Re: The length of the diagonal of a certain rectangle is 8. If the sum of  [#permalink]

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28 Aug 2018, 05:39
Bunuel wrote:
The length of the diagonal of a certain rectangle is 8. If the sum of the lengths of the sides is 10, what is the area of the rectangle?

A. 18
B. 36
C. 64
D. 80
E. It cannot be determined.

The length of the diagonal of a certain rectangle is 8 i,e d=8

a+b=10 --> (1)

(a+b)^2=100

a^2+b^2+2ab=100

we know that

a^2+b^2 = d^2

64+2ab=100

2ab=36

ab=18

Hence A
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The length of the diagonal of a certain rectangle is 8. If the sum of  [#permalink]

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28 Aug 2018, 05:47
Bunuel wrote:
The length of the diagonal of a certain rectangle is 8. If the sum of the lengths of the sides is 10, what is the area of the rectangle?

A. 18
B. 36
C. 64
D. 80
E. It cannot be determined.

Given, Diagonal=$$\sqrt{l^2+w^2}=8$$ Or, $$l^2+w^2=8^2$$
Given, sum of the lengths of the sides is 10 Or (l+w)=10

To find, area=l*w=?

$$(l+w)^2=l^2+w^2+2lw$$
Or, $$10^2=8^2+2lw$$
Or, $$l*w=\frac{10^2-8^2}{2}$$=18

Ans. (A)
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Re: The length of the diagonal of a certain rectangle is 8. If the sum of  [#permalink]

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30 Aug 2018, 18:08
Bunuel wrote:
The length of the diagonal of a certain rectangle is 8. If the sum of the lengths of the sides is 10, what is the area of the rectangle?

A. 18
B. 36
C. 64
D. 80
E. It cannot be determined.

We can create the following equations:

L^2 + W^2 = 8^2

L^2 + W^2 = 64

and

L + W = 10

Squaring both sides of the equation, we have:

(L + W)^2 = 10^2

L^2 + W^2 + 2LW = 100

Substituting, we have:

64 + 2LW = 100

2LW = 36

LW = 18, which is the area of the rectangle.

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Re: The length of the diagonal of a certain rectangle is 8. If the sum of &nbs [#permalink] 30 Aug 2018, 18:08
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