Question

lines $overline{ac}$ and $overline{bd}$ are diagonals of $abcd$. what value of $x$ makes $abcd$ a rectangle if $ac = x + 7$ and $bd = 3x - 5$? (1 point)

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So, we set $AC = BD$.
$x + 7=3x - 5$

Step2: Solve for x

First, move the x - terms to one side and constants to the other side.
$7 + 5=3x - x$
$12 = 2x$
Then, divide both sides by 2.
$x=\frac{12}{2}=6$

Answer:

$x = 6$