Question

ΔABC is an isosceles triangle. ∠A is the vertex angle, and AB = 4x - 14, and AC = x + 10. Find the length of one of the legs.

a. 4x - 14
b. x + 10
c. 2x - 2
d. 3x - 12

Answer 1

In an isosceles triangle, the lengths of the two legs are congruent. By setting the expressions for the lengths of the legs equal to each other, we can find the value of x. Substituting x into either expression will give us the length of one of the legs.

Step-by-step explanation:

In an isosceles triangle, the two legs (AB and AC) are congruent, while the base (BC) is not. We are given that AB = 4x - 14 and AC = x + 10.

Since the two legs are congruent, we can set AB equal to AC and solve for x.

4x - 14 = x + 10

3x = 24

x = 8

Now that we have the value of x, we can substitute it into AB or AC to find the length of one of the legs. Substituting x = 8 into AB, we get:

AB = 4x - 14 = 4(8) - 14 = 32 - 14 = 18

So, the length of one of the legs is 18 units.