Question

the unknown side length
b. p = 1,000 m
x m
150 m
x = 350
mber side lengths. given the area and perimeter, find the
b. a = 36 square m
p = 30 m
w =
36 square m
l =

Explanation:

Step1: Recall rectangle perimeter formula

$P = 2(l + w)$

Step2: Substitute perimeter value

$30 = 2(l + w) \implies l + w = 15$

Step3: Recall rectangle area formula

$A = l \times w$

Step4: Substitute area value

$36 = l \times w$

Step5: Solve for $l$ and $w$

We find two numbers that add to 15 and multiply to 36: $12$ and $3$.

Step1: Use rectangle perimeter formula

$P = 2(x + 150)$

Step2: Substitute $P=1000$

$1000 = 2(x + 150)$

Step3: Solve for $x$

$x + 150 = 500 \implies x = 350$

Answer:

$w = 3$ m, $l = 12$ m (or $w = 12$ m, $l = 3$ m)

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