Question

what is the perimeter of parallelogram wxyz?
the perimeter is \boxed{}. (type an integer or a decimal.)

Explanation:

Step1: Identify equal sides

In parallelogram WXYZ, \(WZ = XY\) and \(WX = YZ\). Given \(WZ = 48\), so \(XY = 48\).

Step2: Find half of WZ

The diagonal intersects \(WZ\) at its midpoint, so half of \(WZ\) is \(\frac{48}{2} = 24\).

Step3: Calculate WX length

Use Pythagorean theorem: \(WX = \sqrt{25^2 - 24^2} = \sqrt{625 - 576} = \sqrt{49} = 7\). So \(YZ = 7\).

Step4: Compute perimeter

Perimeter = \(2(WZ + WX) = 2(48 + 7) = 2×55 = 110\).

Answer:

110