Question

if pq = b and ps = 4b - 54, find the value of b in rhombus qrst.

Explanation:

Step1: Recall rhombus property

In a rhombus, the diagonals bisect each other. So \(PS = 2PQ\).

Step2: Set up the equation

Given \(PQ = b\) and \(PS=4b - 54\), we have \(4b-54 = 2b\).

Step3: Solve the equation for \(b\)

Subtract \(2b\) from both sides: \(4b-2b - 54=2b-2b\), which simplifies to \(2b-54 = 0\). Then add 54 to both sides: \(2b=54\). Divide both sides by 2: \(b = 27\).

Answer:

\(27\)