Question

16 figure mnop, shown below, is a parallelogram. determine the perimeter of mnop. a 30 units b 36 units c 60 units d 72 units

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \(5x = 3x+12\).

Step2: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(5x - 3x=3x + 12-3x\), which gives \(2x=12\). Then divide both sides by \(2\): \(x = 6\).

Step3: Find the lengths of the sides

One side \(MN = 6\). The other side \(MP=5x\), substituting \(x = 6\), we get \(MP=5\times6 = 30\).

Step4: Calculate the perimeter

The perimeter \(P\) of a parallelogram is \(P = 2(a + b)\) (where \(a\) and \(b\) are adjacent sides). Here \(a = 6\) and \(b = 30\), so \(P=2(6 + 30)=2\times36=72\).

Answer:

D. 72 units