Question

If ABC is an isosceles triangle, B is the vertex, ab = 4x + 8, BC = 7x - 10, and AC = 10x - 10, find the value of x and the length of each triangle.

a) x = 4, AB = 20, BC = 22, AC = 30
b) x = 6, AB = 28, BC = 42, AC = 50
c) x = 2, AB = 12, BC = 4, AC = 10
d) x = 8, AB = 36, BC = 62, AC = 70

Answer 1

The expressions for the equal sides equal to each other and solving for x, we found the value of x to be 6.

The correct answer is b) x = 6, AB = 28, BC = 42, AC = 50.

Explanation:

In an isosceles triangle, two sides have equal lengths. Here, AB and AC are the equal sides, given by ab = 4x + 8 and AC = 10x - 10, respectively. Setting them equal to each other, we get:

[4x + 8 = 10x - 10.]

Solving this equation, we find x = 6. Now that we have the value of x, we can substitute it back into the expressions for AB, BC, and AC to find their lengths:

[AB = 4(6) + 8 = 28, ]

[BC = 7(6) - 10 = 42, ]

[AC = 10(6) - 10 = 50.]

So, the lengths of the sides are AB = 28, BC = 42, and AC = 50, confirming that option b) is correct.

In summary, by setting the expressions for the equal sides equal to each other and solving for x, we found the value of x to be 6. Substituting this back into the expressions for the side lengths, we confirmed that the lengths of the sides are AB = 28, BC = 42, and AC = 50, matching option b).