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 = side²So if the area of a small square is 16, then we know that each side of that square has length
4Likewise, if the area of the large square is 36, then we know that each side of that square has length
6At this point, if we focus on one of the small right triangles...
... we can conclude that it has a height of
2This means the right triangle has a height of
2, and a base of length
4When we use the Pythagorean theorem to calculate the length of the hypotenuse, we get
2√5At 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
Answer: C
Cheers,
Brent
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