Question

Two corners of an isosceles triangle are at `(4 ,3 )` and `(9 ,5 )`. If the triangle's area is `64`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides are (5.3852, 23.9208, 24.9208)

Explanation:

Length `a = sqrt((9-4)^2 + (5-3)^2) = sqrt 29 = 5.3852`

Area of `Delta = 64`
`:. h = (Area) / (a/2) = 64 / (5.3852/2) = 64 / 2.6926 = 23.7688`
`side b = sqrt((a/2)^2 + h^2) = sqrt((2.6926)^2 + (23.7688)^2)`
`b = 23.9208`

Since the triangle is isosceles, third side is also `= b = 23.9208`

Measure of the three sides are (5.3852, 23.9208, 23.9208)