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

Answer: C

Cheers,
Brent
_________________

Since the areas of the squares are given, we can easily know the lengths of the sides, which will be the square root of the area.



We would thus have the length for QP = TU = 4

The length of RS = 6

The length of PU = 4 + 6 + 4 = 14

Now, we only need the lengths of QR and ST.

We can see that the base of the triangle is 4 and its height is 2.

The hypotenuse QR will be \(2\sqrt{5}\) = hypotenuse ST

The perimeter can now be calculated by summing all the lengths

Perimeter = 4 + 4 + 6 + 4 + 4 + \(2\sqrt{5}\) + 6 + \(2\sqrt{5}\)

= 16 + 12 + \(4\sqrt{5}\)

= 28 + \(4\sqrt{5}\)

The Answer is Choice C
_________________

You could rotate the image

Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.