Question

what is bc? bc =

Explanation:

Step1: Identify congruent triangles

Since there is a right - angle and two equal side lengths (CD = DE = 30), we can assume that \(\triangle BCD\cong\triangle BED\) (by Hypotenuse - Leg congruence in right - triangles if the right - angled triangles share a common hypotenuse and one leg is equal). So \(BC=BE\).

Step2: Set up an equation

We know that \(BC = a\) and \(BE=3a - 50\). Since \(BC = BE\), we set up the equation \(a=3a - 50\).

Step3: Solve the equation for \(a\)

Subtract \(a\) from both sides: \(0 = 3a - a-50\), which simplifies to \(0 = 2a-50\). Then add 50 to both sides: \(2a=50\). Divide both sides by 2: \(a = 25\).

Step4: Find the length of \(BC\)

Since \(BC=a\), then \(BC = 25\).

Answer:

25