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Mehreen F.

asked • 02/22/13

If the right angled triangle t, with sides of length a and b and hypotenuse of length c, has area equal to c^2/4, then t is an isosceles triangle.

discrete math

Bhadra P.

Given: Angle t is right angle, a = b , 

Since t is Rt angle, side a is perpendicular to side b or equivalent to height

Therefore, area (A) = 1/2 a. b =  1/2 a^2 or 1/2 b^2 ...   ....    ....   .....     .....  (1)

Also, c^2= a^2+ b^2 = 2a^2 or 2b^2 is given for Rt angled triangle.

Therefore,  by dividing both sides by 2  we get a^2 = 1/2 c^2.   ...    ....    ... (2)

By substitution this value from (2) in (1) above, we get

A = 1/2 . 1/2 c^2 = 1/4 c^2

i hope it is clear enough.

Bhadra Panta

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02/22/13

Jacob W.

There is the additional necessary condition that the triangle is isosceles for this explanation to be valid. The fact that there is a right triangle does not guarantee that a=b. (Note 3,4,5 right triangles for example.) The right angle simply validates the Pythagorean theorem for the area of the triangle.

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02/22/13

4 Answers By Expert Tutors

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Johanna R. answered • 02/23/13

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Bhadra P. answered • 02/22/13

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Jacob W. answered • 02/22/13

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