Question

In triangle LMN, △LMN, angle L ≅ angle N, ∠L≅∠N, MN = 7, and NL = 10. Find LM.

a) 17
b) 14
c) 7
d) 3

Answer 1

In triangle LMN, we are given angle L is congruent to angle N, MN = 7, and NL = 10. We need to find the length of side LM. Since triangle LMN is an isosceles triangle, with two sides of equal length, we can solve for the length of LM by setting up an equation and simplifying.

Step-by-step explanation:

In triangle LMN, we are given that angle L is congruent to angle N, MN = 7, and NL = 10. We need to find the length of side LM.

Since angle L is congruent to angle N, it means that angle M is also congruent to angle N. Therefore, triangle LMN is an isosceles triangle, with two sides of equal length.

Let's denote the length of side LM as x. Since triangle LMN is isosceles, we have x + x + 10 = 7. Solving this equation, we find that x = -3, which is not a valid length for a side of a triangle. Therefore, there is no valid length for side LM.