Question

Two corners of an isosceles triangle are at `(4 ,9 )` and `(9 ,3 )`. If the triangle's area is `64`, what are the lengths of the triangle's sides?

Answer 1

The sides are:
Base, `b = bar(AB) = 7.8`
Equal sides, `bar(AC) = bar(BC) = 16.8`

Explanation:

`A_Delta = 1/2 bh = 64`
Using the distance formula find b...
`b = sqrt((x_2-x_1)^2 + (y_2 - y_1)^2)`
`x_1 = 4; x_2 = 9; y_1 = 9; y_2 = 3`
substitute and find h:
`b = sqrt(25 + 36) = sqrt(61) ~~ 7.81`
`h = 2(64)/sqrt(61) = 16.4`
Now using Pythagoras theorem find the sides, `barAC`:
`barAC = sqrt(61/4 + 128^2/61) = sqrt((3,721 + 65,536)/2) = 16.8`