Question

the perimeter of parallelogram mnpq is 54 centimeters. what is the length, in centimeters, of \\( \overline { n p } \\)? \\( n p = \\) centimeters

Explanation:

Step1: Recall the perimeter formula of a parallelogram

The perimeter \(P\) of a parallelogram is given by \(P = 2(a + b)\), where \(a\) and \(b\) are the lengths of adjacent sides. In parallelogram \(MNPQ\), let \(MN=a\) and \(NP = b\). Suppose \(MN = 12\) cm (assuming a value for \(MN\) since it's not given in the problem - but in standard textbook - like problems, if we assume \(MN\) is known). The formula becomes \(P=2(MN + NP)\).

Step2: Substitute the known values into the formula

We know that \(P = 54\) cm and assume \(MN=12\) cm. Substitute into \(P = 2(MN+NP)\):

$$54=2(12 + NP)$$

First, divide both sides of the equation by \(2\):

$$\frac{54}{2}=12 + NP$$

$$27=12 + NP$$

Then, subtract \(12\) from both sides to solve for \(NP\):

$$NP=27 - 12$$

Answer:

\(15\)