Question

13 the diagram below shows parallelogram mnpq and one of its dimensions. the perimeter of parallelogram mnpq is 54 centimeters. what is the length, in centimeters, of \\( \overline { n p } \\)?

Explanation:

Step1: Recall the perimeter formula of a parallelogram

The perimeter \(P\) of a parallelogram is \(P = 2(a + b)\), where \(a\) and \(b\) are the lengths of adjacent sides. In parallelogram \(MNPQ\), let \(a=\overline{MN}=12\) cm and \(b = \overline{NP}\). Given \(P = 54\) cm.

Step2: Substitute values into the formula

Substitute \(P = 54\) and \(a = 12\) into \(P=2(a + b)\). We get \(54=2(12 + b)\).
First, divide both sides of the equation by \(2\): \(\frac{54}{2}=12 + b\). So, \(27=12 + b\).
Then, solve for \(b\) (which is \(\overline{NP}\)) by subtracting \(12\) from both sides: \(b=27 - 12\).

Answer:

\(15\) centimeters