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 `3` and the triangle has an area of `45`. What are the lengths of sides A and B?

Answer 1

The length of sides `A and B` are `30.04(2dp) unit` each.

Explanation:

Here the Isocelles triangle have base `C=3` and the legs as sides `A and B`. The area is `A_t=45`
We know area of triangle as `A_t =1/2 * C . h` where h is altitude of the triangle. `1/2*3*h=45 or h= 90/3=30`
In isocelles triangle altitude touches the base (C) at mid point (D) and is perpendicular to the base. So applying pythagorus theorem we get `A^2 =30^2+ (3/2)^2 or A=sqrt (900+2.25)=30.04(2dp)=B`

The length of sides `A and B` are `30.04(2dp) unit` each.[Ans]