Question

cad is congruent to bad by the hypotenuse leg theorem. given that ca = 8 + 3x and ba = 4 + x, what is x?

Explanation:

Step1: Set up the equation

Since \(\triangle CAD\cong\triangle BAD\) by the hypotenuse - leg theorem, \(CA = BA\). So, \(8 + 3x=4 + x\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(8+3x - x=4+x - x\), which simplifies to \(8 + 2x=4\).
Subtract \(8\) from both sides: \(8+2x - 8=4 - 8\), getting \(2x=-4\).
Divide both sides by \(2\): \(x=\frac{-4}{2}\).

Answer:

\(x = - 2\)