Math CentralQuandaries & Queries


Question from prateet, a student:

the area of an isosceles triangle is 60 sq cm and one of its equal sides is 13 cm. Find the base of the triangle.


In my diagram D is the midpoint of BC, h is the height of the triangle ABC ad B is half its base, both of these are in centimeters.


Since the area of a triangle is half the base times the height the area of the triangle ABC is b × c square centimeters. Thus

b × c = 60 square centimeters.

Find a second equation relating b and h by using Pythagoras theorem on the right triangle ADC.

Solve the pair of equations for b and h.


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