Question

polygon abcd ≡ polygon pqrs. bc = 6x + 5, and qr = 5x + 7. find the value of x and bc.

Explanation:

Step1: Use the property of congruent polygons

Since polygon \(ABCD\cong\) polygon \(PQRS\), their corresponding sides are equal. So \(BC = QR\).

Step2: Set up the equation

Given \(BC = 6x + 5\) and \(QR=5x + 7\), we have the equation \(6x + 5=5x + 7\).

Step3: Solve for \(x\)

Subtract \(5x\) from both sides: \(6x-5x+5 = 5x-5x + 7\), which simplifies to \(x+5=7\).
Then subtract \(5\) from both sides: \(x+5 - 5=7 - 5\), so \(x = 2\).

Step4: Find the length of \(BC\)

Substitute \(x = 2\) into the expression for \(BC\). \(BC=6x + 5\), so \(BC=6\times2+5=12 + 5=17\).

Answer:

\(x = 2\) and \(BC = 17\)