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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] New post 13 Mar 2020, 17:22
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#greprepclub In the figure above, region PQRSTU consists of three.jpg
#greprepclub In the figure above, region PQRSTU consists of three.jpg [ 13.03 KiB | Viewed 203 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. \(34 +4 \sqrt{5}\)


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[Reveal] Spoiler: OA

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Re: In the figure above, region PQRSTU consists of three square [#permalink] New post 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...
Image
... 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
Image

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

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

Answer: C

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

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