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

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Math Expert
Joined: 02 Sep 2009
Posts: 43347
If the area of ∆ PQR above is 32, what is the length of PR? [#permalink]

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17 Aug 2017, 22:35
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If the area of ∆ PQR above is 32, what is the length of PR?

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

[Reveal] Spoiler:
Attachment:

2017-08-18_1026_001.png [ 3.91 KiB | Viewed 571 times ]
[Reveal] Spoiler: OA

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GMAT 1: 660 Q50 V29
Re: If the area of ∆ PQR above is 32, what is the length of PR? [#permalink]

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17 Aug 2017, 23:14
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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Joined: 14 Sep 2016
Posts: 149
Re: If the area of ∆ PQR above is 32, what is the length of PR? [#permalink]

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18 Aug 2017, 02:03
45-45-90 triangle

we get height = base

so, .5 * x^2 = 32

X = 8
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Joined: 22 May 2016
Posts: 1259
If the area of ∆ PQR above is 32, what is the length of PR? [#permalink]

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18 Aug 2017, 10:57
Bunuel wrote:

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

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

[Reveal] Spoiler:
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

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If the area of ∆ PQR above is 32, what is the length of PR? [#permalink]

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18 Aug 2017, 19:30

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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If the area of ∆ PQR above is 32, what is the length of PR?   [#permalink] 18 Aug 2017, 19:30
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