Question

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of `9` and the triangle has an area of `90`. What are the lengths of sides A and B?

Answer 1

Lengths of side A and B are `20.5` units.

Explanation:

Let the sides A and B be `a` units each. As side C has a length of `9` units, one can draw a perpendicular from point opposite which divides the side C in two equal parts.

Hence, height of perpendicular using Pythagoras theorem will be

`sqrt(a^2-(9/2)^2)` and as area of triangle is `90` units

`sqrt(a^2-(9/2)^2)xx9/2=90`

Hence `sqrt(a^2-(9/2)^2)=90xx2/9=20`

or `a^2-(9/2)^2=400`

`a^2=400+81/4=1681/4`

or `a=41/2=20.5`

Lengths of side A and B are `20.5` units.