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

Question

https://gmatclub.com/forum/download/file.php?id=37008 If the area of ∆ PQR above is 32, what is the length of PR? (A) 2 (B) 7 (C) 8 (D) 16 (E) 32 2017-08-18_1026_001.png

anjanikari · Answer

Answer C 
Area =32
Given triangle is right angled triangle. And one angle is 45. From this we will get angle pqr which is 45. So the triangle is isosceles right triangle. 
So area = 1/2 * pr*pr=32
Pr = 8

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kunalsinghNS · Answer

45-45-90 triangle

we get height = base

so, .5 * x^2 = 32

X = 8

generis · Answer

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

pushpitkc · Answer

https://gmatclub.com/forum/download/file.php?id=37008

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)

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

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

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