Question

1. qrst is a rectangle. if rt = 4x - 16 and sq = x + 5, find the value of x.

4
2
7
14

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. Here, RT and SQ are diagonals of rectangle QRST, so RT = SQ.

Step2: Set up the equation

Set up the equation $4x - 16=x + 5$.

Step3: Solve for x

Subtract x from both sides: $4x-x-16=x - x+ 5$, which simplifies to $3x-16 = 5$. Then add 16 to both sides: $3x-16 + 16=5 + 16$, getting $3x=21$. Divide both sides by 3: $\frac{3x}{3}=\frac{21}{3}$, so $x = 7$.

Answer:

7