Question

Solve each problem given the information.

12. If ΔJKL is an equilateral triangle, JK = 13x + 5, KL = 17x - 19, and JL = 8x + 35, find x and the measure of each side.

Answer 1

x = 6 , JK = KL = JL = 83

Explanation:

given Δ JKL is equilateral then the 3 sides are congruent.

equate any 2 of the 3 sides and solve for x

KL = JL , that is

17x - 19 = 8x + 35 ( subtract 8x from both sides )

9x - 19 = 35 ( add 19 to both sides )

9x = 54 ( divide both sides by 9 )

x = 6

then

JL = 8x + 35 = 8(6) + 35 = 48 + 35 = 83

since the 3 sides are congruent , then

JK = KL = JL = 83