Question

Two corners of an isosceles triangle are at `(5 ,3 )` and `(6 ,7 )`. If the triangle's area is `4`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides are (4.1231, 2.831, 2.831)

Explanation:

Length `a = sqrt((6-5)^2 + (7-5)32) = sqrt 17 = 4.1231`

Area of `Delta = 4`
`:. h = (Area) / (a/2) = 4 / (4.1231/2) = 4 / 2.0616 = 1.9402`
`side b = sqrt((a/2)^2 + h^2) = sqrt((2.0616)^2 + (1.9402)^2)`
`b = 2.831`

Since the triangle is isosceles, third side is also `= b = 2.831`

Measure of the three sides are (4.1231, 2.831, 2.831)