Question

in order for the parallelogram to be a rectangle, x = ?. diagonal $overline{ac}=5x - 17$ diagonal $overline{bd}=2x - 2$

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So we set $\overline{AC}=\overline{BD}$, giving the equation $5x - 17=2x - 2$.

Step2: Isolate x - terms

Subtract $2x$ from both sides: $5x-2x - 17=2x-2x - 2$, which simplifies to $3x - 17=- 2$.

Step3: Isolate the constant

Add 17 to both sides: $3x-17 + 17=-2 + 17$, resulting in $3x=15$.

Step4: Solve for x

Divide both sides by 3: $\frac{3x}{3}=\frac{15}{3}$, so $x = 5$.

Answer:

$5$