Question

Triangles A B C and H G L are congruent. Angles A B C and H G L are right angles. The length of hypotenuse A C is 15 and the length of hypotenuse H L is 3 x + 3. The length of A B is 9 and the length of B C is 12. The length of G L is 2 x + 1. For the triangles to be congruent by HL, what must be the value of x? 2 3 4 7

Answer 1

x = 4

Therefore, for the triangles to be congruent by HL, the value of x must be 4.

Explanation:

Given: ΔABC and ΔHGL are congruent. ∠ABC = ∠HGL = 90°.

Length of hypotenuse AC = 15

Length of hypotenuse HL = 3x + 3

Length of AB = 9, Length of BC = 12 and Length of GL = 2x + 1.

Sol: ∵ ΔABC ≅ ΔHGL

Length of HL = Length of AC (corresponding parts of congruent triangles)

3x + 3 = 15

3x = 15 - 3

3x = 12

x = 12/3 = 4

Therefore, for the triangles to be congruent by HL, the value of x must be 4.