Question

Two corners of an isosceles triangle are at `(8 ,5 )` and `(6 ,1 )`. If the triangle's area is `12`, what are the lengths of the triangle's sides?

Answer 1

Measure of the three sides of the `Delta` are `color(red)(4.4721, 2.8636, 2.8636`

Explanation:

Length `a = sqrt((6-8)^2 + (1-5)^2) = sqrt 20 = 4.4721`

Area of `Delta = 12`
`:. h = (Area) / (a/2) = 12 / (4.4721/2) = 4/2.2361 = 1.7888`

`side b = sqrt((a/2)^2 + h^2) = sqrt((2.2361)^2 + (1.7888)^2)`
`b = 2.8636`

Since the triangle is isosceles, third side is also `= b = 2.8636`