Question

if qr = rs = 99, qt = p + 78, and st = 7p, what is the
p =

Explanation:

Step1: Apply perpendicular - bisector theorem

Since $QR = RS$ and the line through $R$ is perpendicular to $QS$ (right - angle at $T$), by the perpendicular - bisector theorem, $QT=ST$.

Step2: Set up the equation

Set up the equation $p + 78=7p$.

Step3: Solve for $p$

Subtract $p$ from both sides: $78 = 7p-p$.
Simplify the right - hand side: $78=6p$.
Divide both sides by 6: $p=\frac{78}{6}=13$.

Answer:

$13$