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 `4` and the triangle has an area of `42`. What are the lengths of sides A and B?

Answer 1

Length of sides A & B are `21.1(1dp)` unit

Explanation:

Let Altitude (h) be drawn from junction of sides `A & B` on Side `C`. We know area of the triangle is `1/2*C*h=42 or 1/2*4*h=42:.h=21`The altitude meets side C at midpoint and perpendicular to C.`:.h^2+(C/2)^2=A^2 :.A^2=21^2+(4/2)^2=441+4=445 :.A=B=sqrt445=21.1(1dp)`unit