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

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Math Expert
Joined: 02 Sep 2009
Posts: 64242
In the figure above, region PQRSTU consists of three square regions an  [#permalink]

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22 Oct 2019, 21:29
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25% (medium)

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86% (01:55) correct 14% (02:07) wrong based on 42 sessions

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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√5
(B) 28 + 2√5
(C) 28 + 4√5
(D) 34 + 2√5
(E) 34 + 4√5

Attachment:

2017-11-10_1034.png [ 6.98 KiB | Viewed 446 times ]

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Re: In the figure above, region PQRSTU consists of three square regions an  [#permalink]

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22 Oct 2019, 22:32
for side QR and ST value will be 2√5 each
perimeter ;
28 + 4√5

IMO C

Bunuel wrote:

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√5
(B) 28 + 2√5
(C) 28 + 4√5
(D) 34 + 2√5
(E) 34 + 4√5

Attachment:
2017-11-10_1034.png
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4879
GMAT 1: 770 Q49 V46
Re: In the figure above, region PQRSTU consists of three square regions an  [#permalink]

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26 Mar 2020, 09:50
Top Contributor
Bunuel wrote:

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√5
(B) 28 + 2√5
(C) 28 + 4√5
(D) 34 + 2√5
(E) 34 + 4√5

Attachment:
2017-11-10_1034.png

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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Re: In the figure above, region PQRSTU consists of three square regions an   [#permalink] 26 Mar 2020, 09:50

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

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