SOLUTION: In triangle KLM, if ∠K ≅ ∠L , KL = 9x – 40, LM = 7x – 37, and KM = 3x + 23, find x and the measure of each side.

Algebra ->  Triangles -> SOLUTION: In triangle KLM, if ∠K ≅ ∠L , KL = 9x – 40, LM = 7x – 37, and KM = 3x + 23, find x and the measure of each side.       Log On


   

Question 1102972: In triangle KLM, if ∠K ≅ ∠L , KL = 9x – 40, LM = 7x – 37, and KM = 3x + 23, find x and the
measure of each side.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
triangle KLM is an isosceles triangle with angle K congruent to angle L.

therefore, the sides opposite these angles are congruent.

side KM is opposite angle L.
side ML is opposite angle K

therefore, side KM is congruent to side ML.

the length of side KM is equal to 3x + 23
the length of side ML is equal to 7x - 37

therefore, 3x + 23 = 7x - 37

solve for x to get x = 15

3x + 23 = 3*15 + 23 = 68 = length of KM.
7x - 37 = 7*15 - 37 = 68 = length of ML.

9x -40 = 9*15 - 40 = 95 = length of KL.

your solution is that x = 15 and the length of each side is 68 for the two congruent sides and 95 for the side opposite the vertex of the isosceles triangle.

here's some basic information regarding isosceles triangles plus other types.

https://www.mathsisfun.com/definitions/isosceles-triangle.html