Question

If B is the midpoint of AC, and AB = 4x - 2 and AC = 20 ft, then how long is AB and BC?

a) AB = 4 ft, BC = 16 ft
b) AB = 6 ft, BC = 14 ft
c) AB = 8 ft, BC = 12 ft
d) AB = 10 ft, BC = 10 ft

Answer 1

To find the lengths of AB and BC when B is the midpoint of AC, solve the equation 2(AB) = AC with the given values. The calculations lead to AB and BC each being 10 ft, so the correct answer is (d) AB = 10 ft, BC = 10 ft.

Step-by-step explanation:

If B is the midpoint of AC, then AB = BC. Given AB = 4x - 2 and AC = 20 ft, we can write 2(AB) = AC because AB and BC are equal. By substituting AC with 20 ft, we get 2(4x - 2) = 20.

Solving the equation gives us the following steps:

1. Multiply out the left side: 8x - 4 = 20.
2. Add 4 to both sides: 8x = 24.
3. Divide both sides by 8: x = 3.

Now that we know x = 3, we substitute it back into the expression for AB to find the length of AB and BC.

AB = 4(3) - 2, hence AB = 12 - 2 which means AB = 10 ft. As AB = BC, it follows that BC = 10 ft.

Therefore, the correct answer is (d) AB = 10 ft, BC = 10 ft.