Question

Two corners of an isosceles triangle are at `(1 ,7 )` and `(3 ,3 )`. If the triangle's area is `64`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides of the triangle are (4.4721, 28.7085, 28.7085)

Explanation:

Length `a = sqrt((3-1)^2 + (3-7)^2) = sqrt 20 = 4.4721`

Area of `Delta = 64`
`:. h = (Area) / (a/2) = 64 / (4.4721/2) = 64 / 2.2361 = 28.6213`
`side b = sqrt((a/2)^2 + h^2) = sqrt((2.2361)^2 + (28.6213)^2)`
`b = 28.7085`

Since the triangle is isosceles, third side is also `= b = 28.7085`

Measure of the three sides are (4.4721, 28.7085, 28.7085)