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Bunuel

If the area of ∆ PQR above is 32, what is the length of PR?

(A) 2
(B) 7
(C) 8
(D) 16
(E) 32


Attachment:
2017-08-18_1026_001.png
Third angle must = 45°; this is an isosceles right triangle

Area of isosceles right triangle, where a = leg (i.e., not hypotenuse) is \(\frac{a^2}{2}\)

\(\frac{a^2}{2}\) = 32

\(a^2\) = 64

a = 8 = PR

Answer C
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Given data: Area of ∆ PQR above is 32.

Since, one of the angles is 45 degree, the right angled triangle is isosceles.
The ratios of the sides are \(1:1:\sqrt{2}\)

Let PR = PQ = x(which is both the Base and the Height)

Since area is 32, \(\frac{1}{2} * x^2 = 32\)
\(x^2 = 64 => x = 8\)

Therefore, the length of PR is 8(Option C)
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