Question

if pq = w and ps = 3w - 68, find ps in rectangle qrst. ps =

Explanation:

Step1: Recall rectangle property

In a rectangle, opposite - sides are equal. Let's assume that \(PQ\) and \(PS\) are adjacent sides of the rectangle. If we consider the relationship between the sides based on the given information, we might assume that there is some other condition. A common property of rectangles is that the diagonals are equal and bisect each other. But if we assume that \(PQ\) and \(PS\) are related in a way that \(PQ = PS\) (a special case, maybe a square which is a special rectangle). So we set up the equation \(w=3w - 68\).

Step2: Solve the equation for \(w\)

Subtract \(w\) from both sides: \(0 = 3w - w-68\), which simplifies to \(0 = 2w - 68\). Then add 68 to both sides: \(2w=68\). Divide both sides by 2: \(w = 34\).

Step3: Find the value of \(PS\)

Since \(PS = 3w - 68\), substitute \(w = 34\) into the expression for \(PS\). \(PS=3\times34 - 68\). First, calculate \(3\times34 = 102\), then \(102-68 = 34\).

Answer:

34