Question

Two corners of an isosceles triangle are at `(2 ,4 )` and `(3 ,8 )`. If the triangle's area is `18`, what are the lengths of the triangle's sides?

Answer 1

First find the length of the base, then solve for the height using the area of 18.

Explanation:

Using the distance formula ...

length of base `=sqrt[(3-2)^2+(8-4)^2]=sqrt17`

Next, find the height ...

Triangle Area = `(1/2) xx("base")xx("height")`

`18=(1/2)xxsqrt17xx("height")`

height `=36/sqrt17`

Finally, use Pythagorean theorem to find the length of the two equal sides ...

`(height)^2+[(1/2)(base)]^2=(side)^2`

`(36/sqrt17)^2+[(1/2)(sqrt17)]^2=(side)^2`

Sides `=sqrt(5473/68)~~8.97`

In summary, the isosceles triangle has two equal sides of length `~~8.97` and a base length of `sqrt17`

Hope that helped