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# In the figure shown, what is the value of x?

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Math Expert
Joined: 02 Sep 2009
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In the figure shown, what is the value of x?  [#permalink]

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26 Mar 2018, 23:25
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15% (low)

Question Stats:

86% (01:00) correct 14% (01:39) wrong based on 49 sessions

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In the figure shown, what is the value of x?

(1) a = b = 4

(2) $$c = 4\sqrt{2}$$

Attachment:

2018-03-27_1023.png [ 8.26 KiB | Viewed 756 times ]

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Re: In the figure shown, what is the value of x?  [#permalink]

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26 Mar 2018, 23:26
Bunuel wrote:

In the figure shown, what is the value of x?

(1) a = b = 4

(2) $$c = 4\sqrt{2}$$

Attachment:
2018-03-27_1023.png

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Re: In the figure shown, what is the value of x?  [#permalink]

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27 Mar 2018, 00:10
Bunuel wrote:

In the figure shown, what is the value of x?

(1) a = b = 4

(2) $$c = 4\sqrt{2}$$

Attachment:
2018-03-27_1023.png

From the image we know that 3 angles of the quadrilateral on the right are 90deg .. so it is a rectangle & it can be a square if adjacent sides are equal
Also the triangle to the left is a right angled triangle.

We need to find x which is the sum of lengths of the base of the triangle and side of the rectangle.

(1) a = b= 4 meaning.. adjacent sides of rectangle are equal in length! It is a square. Not sufficient as we know nothing about the triangle except for one angle ( 90 deg) and one side ( 4 - side common with the square)

(2) $$c = 4\sqrt{2}$$ Not sufficient as we do not know the base of the triangle or anything about the rectangle to the right.

(1) + (2) together ... We know the base of the square is 4 in length.. & .. from Pythagoras theorem we can find the base of the triangle. Sufficient!

Hence Option C is correct.
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In the figure shown, what is the value of x?  [#permalink]

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27 Mar 2018, 00:26
Attachment:

2018-03-27_1023.png [ 12.24 KiB | Viewed 652 times ]

In the figure shown, what is the value of x?

(1) a = b = 4
If a = b = 4, PQRS has to be a square. Here, RS = 4.
But, we have no idea about the length of TR (Insufficient)

(2) $$c = 4\sqrt{2}$$
With the information c = $$4\sqrt{2}$$, we can't determine
the value of TR. Also, we have no information about RS (Insufficient)

When we combine the information from both the statements,
PR = 4(because PR is the side of a square) and the right triangle
has to be an isosceles right-angled triangle. Therefore, TR = $$4\sqrt{2}$$
The value of x = RS + TR = 4 + $$4\sqrt{2}$$ (Sufficient - Option C)
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In the figure shown, what is the value of x?   [#permalink] 27 Mar 2018, 00:26
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