Question

qrst is a rectangle. if rt = 2x - 14 and sq = x + 8, find the value of x.
22
19
7
12

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So, if \(RT\) and \(SQ\) are diagonals of rectangle \(QRST\), then \(RT = SQ\).

Step2: Set up the equation

We are given \(RT=2x - 14\) and \(SQ=x + 8\). Setting them equal gives \(2x-14=x + 8\).

Step3: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(2x-x-14=x - x+8\), which simplifies to \(x-14 = 8\). Then add 14 to both sides: \(x-14 + 14=8 + 14\), so \(x=22\).

Answer:

22