Question

10. AGHI is an isosceles triangle with GIHI. 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

x = 14 , G H = 17 units , HI = 39 units , GI = 39 units

Explanation:

Here, the given triangle GHI is an isosceles triangle with GI = HI .

G H = 3 more than x = 3 + x

HI = 17 less than four times x = 4 x - 17

GI = 45 less than six times x = 6 x - 45

Now, given HI = GI

⇒ 4 x - 17 = 6 x - 45

or, -1 7 + 45 = 6 x - 4 x

or, 2 x = 28

or, x = 28/2 = 14

⇒ x = 14

Hence the measure of G H = 3 + x = 3 + 14 = 17 units

HI = 4 x - 17 = 4(14) - 17 = 39 units

GI = 6 x -45 = 6(14) - 45 = 39 units