Question

Two corners of an isosceles triangle are at `(1 ,2 )` and `(3 ,1 )`. If the triangle's area is `12`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides are (2.2361, 10.7906, 10.7906)

Explanation:

Length `a = sqrt((3-1)^2 + (1-2)^2) = sqrt 5 = 2.2361`

Area of `Delta = 12`
`:. h = (Area) / (a/2) = 12 / (2.2361/2) = 12 / 1.1181 = 10.7325`
`side b = sqrt((a/2)^2 + h^2) = sqrt((1.1181)^2 + (10.7325)^2)`
`b = 10.7906`

Since the triangle is isosceles, third side is also `= b = 10.7906`

Measure of the three sides are (2.2361, 10.7906, 10.7906)