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Find the area of an isosceles right triangle?

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Senior Manager
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Joined: 02 Jan 2017
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Find the area of an isosceles right triangle? [#permalink]

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New post 14 Mar 2017, 09:06
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D
E

Difficulty:

  35% (medium)

Question Stats:

53% (00:50) correct 47% (00:44) wrong based on 49 sessions

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Find the area of an isosceles right triangle?

(1) The length of one of its legs is 10 cm

(2) The length of its hypotenuse is 10√2


Source: www.analyzemath.com/gmat/gmatdata1.html
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Magoosh GMAT Instructor
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Re: Find the area of an isosceles right triangle? [#permalink]

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New post 14 Mar 2017, 12:17
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vikasp99 wrote:
Find the area of an isosceles right triangle?

(1) The length of one of its legs is 10 cm

(2) The length of its hypotenuse is 10√2

Dear vikasp99,

I'm happy to respond. :-)

This question is much much easier than what the GMAT would ask. The GMAT expects you to have memorized the ratios of the two special right triangles, the 30-60-90 triangle and the 45-45-90 triangle. See:
The GMAT’s Favorite Triangles

Since the sides in the 45-45-90 triangle always have the ratios \(1 - 1 - \sqrt{2}\), if we have the length of any one side, we instantly know the other sides.

Thus, each statement on its own is sufficient. OA = (D)

Does all this make sense?
Mike :-)
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Mike McGarry
Magoosh Test Prep

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Re: Find the area of an isosceles right triangle? [#permalink]

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New post 15 Mar 2017, 02:39
let the sides of the the triangle be a, a and h
h^2 = a^2 + a^2
area = a^2 / 2

ST 1: a = 10. therefore the area = 10*10/2 = 50. ANSWER
St 2: h = 10√2. hence a = 10 and area = 10*10/2 = 50. ANSWER

Option D
Re: Find the area of an isosceles right triangle?   [#permalink] 15 Mar 2017, 02:39
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Find the area of an isosceles right triangle?

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