Question

(a) the perimeter of a rectangular parking lot is 300 m. if the width of the parking lot is 67 m, what is its length? length of the parking lot: □ m (b) the area of a rectangular pool is 3795 m². if the length of the pool is 69 m, what is its width? width of the pool: □ m

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $P$ is the perimeter, $l$ is the length and $w$ is the width. Given $P=300$ m and $w = 67$ m. We substitute these values into the formula: $300=2(l + 67)$.

Step2: Solve for length $l$

First, divide both sides of the equation $300 = 2(l + 67)$ by 2: $\frac{300}{2}=l + 67$, so $150=l + 67$. Then subtract 67 from both sides: $l=150 - 67=83$ m.

Step3: Recall area formula for rectangle

The area formula of a rectangle is $A=l\times w$, where $A$ is the area, $l$ is the length and $w$ is the width. Given $A = 3795$ m² and $l=69$ m. We substitute these values into the formula: $3795=69\times w$.

Step4: Solve for width $w$

Divide both sides of the equation $3795 = 69w$ by 69: $w=\frac{3795}{69}=55$ m.

Answer:

Length of the parking lot: 83 m
Width of the pool: 55 m