Question

question 9
a contractor is building a pool labeled abcd on the plans. if ac = 10y + 4 and bd = 13y - 8, what value of y ensures the pool is a rectangle?

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal. So, we set $AC = BD$.
$10y + 4=13y - 8$

Step2: Isolate y - terms

Subtract $10y$ from both sides:
$10y+4 - 10y=13y - 8-10y$
$4 = 3y-8$

Step3: Solve for y

Add 8 to both sides:
$4 + 8=3y-8 + 8$
$12 = 3y$
Divide both sides by 3:
$\frac{12}{3}=\frac{3y}{3}$
$y = 4$

Answer:

4