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# In the figure above, region PQRSTU consists of three square

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In the figure above, region PQRSTU consists of three square [#permalink]  13 Mar 2020, 17:22
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80% (01:01) correct 20% (01:44) wrong based on 15 sessions
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#greprepclub In the figure above, region PQRSTU consists of three.jpg [ 13.03 KiB | Viewed 202 times ]

In the figure above, region $$PQRSTU$$ consists of three square regions and two triangular regions. If the square regions have areas 16, 36, and 16, what is the perimeter of $$PQRSTU$$?

A. $$22+4 \sqrt{5}$$

B. $$28+2 \sqrt{5}$$

C. $$28+4 \sqrt{5}$$

D. $$34+2 \sqrt{5}$$

E. $$34 +4 \sqrt{5}$$

Kudos for the right answer and explanation
[Reveal] Spoiler: OA

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Re: In the figure above, region PQRSTU consists of three square [#permalink]  26 Mar 2020, 09:51
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Carcass wrote:
Attachment:
#greprepclub In the figure above, region PQRSTU consists of three.jpg

In the figure above, region $$PQRSTU$$ consists of three square regions and two triangular regions. If the square regions have areas 16, 36, and 16, what is the perimeter of $$PQRSTU$$?

A. $$22+4 \sqrt{5}$$

B. $$28+2 \sqrt{5}$$

C. $$28+4 \sqrt{5}$$

D. $$34+2 \sqrt{5}$$

E. $$34 +4 \sqrt{5}$$

Kudos for the right answer and explanation

Area of square = side²
So if the area of a small square is 16, then we know that each side of that square has length 4
Likewise, if the area of the large square is 36, then we know that each side of that square has length 6

At this point, if we focus on one of the small right triangles...

... we can conclude that it has a height of 2

This means the right triangle has a height of 2, and a base of length 4
When we use the Pythagorean theorem to calculate the length of the hypotenuse, we get 2√5

At this point we have enough information to find the length of each side of our figure:

So, the perimeter of PQRSTU = 6 + 2√5 + 4 + 4 + 6 + 4 + 4 + 2√5
= 28 + 4√5

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: In the figure above, region PQRSTU consists of three square   [#permalink] 26 Mar 2020, 09:51
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