Question

10. angle GHI is an isosceles triangle with GI HI. IF GH is three more than x, HI is 17 less than four

times x, and GI is 45 less than six times x, find x and the measure of each side.

Answer 1

GH = 17 units

GI = 39 units

HI = 39 units

Explanation:

We are given the following information in the question:

Triangle GHI is an isosceles triangle.

`GI = HI`

The measures of side are:

`GH = 3 + x\\HI = 4x-17\\GI = 6x - 45`

It is given that

GI = HI

`4x - 17 = 6x -45\\6x - 4x = 45-17\\2x = 28\\x = 14`

Thus, the measures of three sides are:

`GH = 3 + x=14+3 = 17\\HI = 4x-17 = 4(14)-17 = 39\\GI = 6x - 45=6(14) - 45 = 39`