Question

answer the questions below. (a) the perimeter of a rectangular parking lot is 314 m. if the length of the parking lot is 91 m, what is its width? width of the parking lot: m (b) the area of a rectangular pool is 7176 m². if the width of the pool is 78 m, what is its length? length 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 perimeter, $l$ is length and $w$ is width. Given $P=314$ m and $l = 91$ m. First, substitute values into formula: $314=2(91 + w)$.

Step2: Solve for width

Divide both sides of the equation $314 = 2(91+w)$ by 2: $\frac{314}{2}=91 + w$, so $157=91 + w$. Then subtract 91 from both sides: $w=157 - 91$.

Step3: Calculate width value

$w = 66$ m.

Step4: Recall area formula for rectangle

The area formula of a rectangle is $A=l\times w$, where $A$ is area, $l$ is length and $w$ is width. Given $A = 7176$ m² and $w = 78$ m. Substitute values into formula: $7176=l\times78$.

Step5: Solve for length

Divide both sides of the equation $7176=l\times78$ by 78: $l=\frac{7176}{78}$.

Step6: Calculate length value

$l = 92$ m.

Answer:

(a) Width of the parking - lot: 66 m
(b) Length of the pool: 92 m