Question

in parallelogram ( wxyz ), diagonals ( overline{wy} ) and ( overline{xz} ) intersect at ( a ). ( wa = x^{2}-48 ) and ( ay = 2x ). what is ( wy )? enter your answer in the box. ( wy=square ) units

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(WA = AY\).
\(x^{2}-48 = 2x\)

Step2: Rearrange the equation to standard quadratic form

\(x^{2}-2x - 48=0\)

Step3: Factor the quadratic equation

\((x - 8)(x + 6)=0\)

Step4: Solve for \(x\)

\(x-8 = 0\) gives \(x = 8\); \(x + 6=0\) gives \(x=-6\). Since length cannot be negative, we take \(x = 8\).

Step5: Find \(WA\) and \(WY\)

\(WA=x^{2}-48\), substituting \(x = 8\), \(WA=8^{2}-48=64 - 48=16\). Since \(WY=2WA\) (diagonals bisect each other), \(WY = 2\times16\)

Answer:

\(32\)