Question

Two corners of an isosceles triangle are at `(4 ,2 )` and `(6 ,7 )`. If the triangle's area is `3`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides are (5.3852, 2.914, 2.914)

Explanation:

Length `a = sqrt((6-4)^2 + (7-2)^2) = sqrt 29 = 5.3852`

Area of `Delta = 3`
`:. h = (Area) / (a/2) = 3 / (5.3852/2) = 3 / 2.6926 = 1.1142`
`side b = sqrt((a/2)^2 + h^2) = sqrt((2.6926)^2 + (1.1142)^2)`
`b = 2.914`

Since the triangle is isosceles, third side is also `= b = 2.914`

Measure of the three sides are (5.3852, 2.914, 2.914)