Question

the perimeter of the rectangle below is 150 units. find the value of y.

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=5y$, $w = 4y + 3$ and $P=150$. So we have $150=2(5y+(4y + 3))$.

Step2: Simplify the equation

First, simplify the expression inside the parentheses: $5y+(4y + 3)=9y + 3$. Then the equation becomes $150 = 2(9y + 3)$. Distribute the 2: $150=18y+6$.

Step3: Solve for y

Subtract 6 from both sides of the equation: $150 - 6=18y$, so $144 = 18y$. Divide both sides by 18: $y=\frac{144}{18}=8$.

Answer:

$8$