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In above figure, the area of shaded region is 75% of the area of the

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In above figure, the area of shaded region is 75% of the area of the  [#permalink]

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New post 25 Jun 2018, 00:20
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A
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C
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E

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71% (02:34) correct 29% (02:15) wrong based on 29 sessions

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In above figure,the area of shaded region is 75% of the area of the Square. What is the value of x?

A) 5.5
B) 6.5
C) 7.5
D) 8.5
E) 9.5

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Re: In above figure, the area of shaded region is 75% of the area of the  [#permalink]

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New post 25 Jun 2018, 01:06
This question is a beautiful example to use symmetry in Geometry Problems:

Since the Shaded area is 75%, this means the unshaded area is 25%, hence 2*area of triangle = 25% of area of Square

Hence, 2*area of triangle = 25% of 15*15 = 225/4

Area of triangle = 225/8

So (15-x)*(15-x)/2 = 225/8

Or, (15-x)^2= 225/4

Or, 15-x = 15/2

x = 15/2 = 7.5.

Answer = C

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Re: In above figure, the area of shaded region is 75% of the area of the  [#permalink]

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New post 25 Jun 2018, 02:25
Princ wrote:
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Untitled.png

In above figure,the area of shaded region is 75% of the area of the Square. What is the value of x?

A) 5.5
B) 6.5
C) 7.5
D) 8.5
E) 9.5



Cut the square into half as diagonal in the shaded region. Even the shaded and unshaded region are cut into half...
Area of unshaded region if cut into half will , therefore , remain 75% of the triangle thus formed...
Now we have two similar triangle, one unshaded within the second bigger triangle..
If Area are of ratio 1/4:1, the sides will be in ratio of square root..
So x:15=√(1/4):√1 or 1/2:1=x:15....
So x=15/2=7.5
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Re: In above figure, the area of shaded region is 75% of the area of the  [#permalink]

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New post 25 Jun 2018, 03:29
Area of the non-shaded region = 25% of the total area. This means that the two unshaded portions make up for 1/4th the total area.
The unshaded portion can be combined to make a square of side (15-x) units. If this square's area is 1/4th the area of the original square, the side should be 1/2 the original square.

Therefore, 15-x = 15/2 => x = 7.5

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Re: In above figure, the area of shaded region is 75% of the area of the &nbs [#permalink] 25 Jun 2018, 03:29
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