Question

1. if the perimeter of the parallelogram is 158 inches, what is the value of x?

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So \(NP = RQ=(7x + 6)\) and \(PQ=RN=(-3x + 41)\). The perimeter formula of a parallelogram is \(P = 2(a + b)\), where \(a\) and \(b\) are adjacent sides. Here \(P=158\), \(a=(7x + 6)\) and \(b=(-3x + 41)\). So \(158=2[(7x + 6)+(-3x + 41)]\).

Step2: Simplify the equation

First, simplify the expression inside the brackets: \((7x + 6)+(-3x + 41)=7x-3x+6 + 41=4x+47\). Then the equation becomes \(158 = 2(4x + 47)\). Divide both sides by 2: \(\frac{158}{2}=4x + 47\), so \(79=4x + 47\).

Step3: Solve for \(x\)

Subtract 47 from both sides: \(79-47=4x\), \(32 = 4x\). Divide both sides by 4: \(x=\frac{32}{4}\).

Answer:

\(x = 8\)