Question

1. the width of a rectangle garden is 5 feet less than its length. if the perimeter of the garden is 50 ft, write and use an equation to find the dimensions (length and width) of the garden. *hint: use l as the variable for length.

Explanation:

Step1: Define variables

Let the length of the rectangle be $l$ feet. Then the width $w=l - 5$ feet.

Step2: Write perimeter formula

The perimeter formula for a rectangle is $P = 2(l+w)$. Given $P = 50$ feet, substitute $w=l - 5$ into the formula: $50=2(l+(l - 5))$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $50=2(2l-5)$. Then distribute the 2: $50 = 4l-10$.

Step4: Solve for $l$

Add 10 to both sides of the equation: $50 + 10=4l-10 + 10$, which gives $60 = 4l$. Divide both sides by 4: $l=\frac{60}{4}=15$ feet.

Step5: Solve for $w$

Since $w=l - 5$, substitute $l = 15$ into the equation for $w$: $w=15 - 5=10$ feet.

Answer:

Equation: $50=2(l+(l - 5))$
Length: $15$ ft
Width: $10$ ft