Question

Two corners of an isosceles triangle are at `(5 ,2 )` and `(2 ,1 )`. If the triangle's area is `8`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides are (3.1623, 5.3007, 5.3007)

Explanation:

Length `a = sqrt((2-5)^2 + (1-2)^2) = sqrt 10 = 3.1623`

Area of `Delta = 8`
`:. h = (Area) / (a/2) = 8 / (3.1623/2) = 8 / 1.5812 = 5.0594`
`side b = sqrt((a/2)^2 + h^2) = sqrt((1.5812)^2 + (5.0594)^2)`
`b = 5.3007`

Since the triangle is isosceles, third side is also `= b = 5.3007`

Measure of the three sides are (3.1623, 5.3007, 5.3007)