Question

alices backyard is a rectangular piece of property that is twice as long as it is wide. the total area of her yard is 1,000 m². what is the approximate width of her backyard?
a = lw
11.2 m
15.8 m
22.4 m
44.8 m

Explanation:

Step1: Define variables

Let the width be $w$ meters. Since the length $l$ is twice the width, $l = 2w$. The area formula for a rectangle is $A=lw$. Given $A = 1000$ m².

Step2: Substitute into area formula

Substitute $l = 2w$ into $A=lw$, we get $1000=(2w)w=2w^{2}$.

Step3: Solve for $w$

First, divide both sides of the equation $2w^{2}=1000$ by 2: $w^{2}=500$. Then, take the square - root of both sides: $w=\sqrt{500}\approx22.4$ m.

Answer:

C. 22.4 m