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# Find the area of an isosceles right triangle?

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Senior Manager
Joined: 02 Jan 2017
Posts: 312
Find the area of an isosceles right triangle?  [#permalink]

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14 Mar 2017, 09:06
00:00

Difficulty:

35% (medium)

Question Stats:

67% (00:56) correct 33% (00:52) 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
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4494
Re: Find the area of an isosceles right triangle?  [#permalink]

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14 Mar 2017, 12:17
1
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

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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

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