Find the area of an isosceles right triangle?

Question

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

mikemcgarry · Answer

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 :-)

KrishnakumarKA1 · Answer

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

Find the area of an isosceles right triangle?

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