Question

Two corners of an isosceles triangle are at `(8 ,5 )` and `(9 ,1 )`. If the triangle's area is `12`, what are the lengths of the triangle's sides?

Answer 1

`color(maroon)("Lengths of the triangle "a = sqrt 17, b = sqrt(2593 / 68), c = sqrt(2593 / 68)`

Explanation:


`color(red)( B(8,5), C(9,1), A_t = 12`

let `bar(AD) = h`

`bar(BC) = a = sqrt((9-8)^2 + (1-5)^2) = sqrt17`

`Area of triangle " A_t = 12 = (1/2) a *h = (sqrt17 h)/2`

`h = 24 / sqrt17`

`bar(AC) = bar(AB) = b = sqrt((a/2)^2 + h^2)`

`b = sqrt((sqrt17/2)^2 + (24/sqrt17)^2)`

`b = sqrt(17/4 + 576/17) = sqrt(2593/68)`