Question

what is the length of side bc of the triangle?
enter your answer in the box.
□ units
(image of triangle with sides: ac = 2x + 7, ab = 4x - 7, bc = 4x, and angles at c and b equal)

Explanation:

Step1: Identify triangle type

The triangle has two equal angles (at \( C \) and \( B \)), so it's isosceles. Thus, \( AC = AB \).
\( 2x + 7 = 4x - 7 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides: \( 7 = 2x - 7 \)
Add 7 to both sides: \( 14 = 2x \)
Divide by 2: \( x = 7 \)

Step3: Find \( BC \) length

\( BC = 4x \), substitute \( x = 7 \): \( 4(7) = 28 \)

Answer:

28