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 15.8 m 22.4 m 44.8 m 11.23 m

Explanation:

Step1: Define variables

Let the width be $w$ and the length $l = 2w$, and the area $A=1000\ m^{2}$. The area formula for a rectangle is $A = lw$.

Step2: Substitute $l$ into area formula

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

Step3: Solve for $w$

Since $A = 1000\ m^{2}$, then $2w^{2}=1000$. Divide both sides by 2: $w^{2}=\frac{1000}{2}=500$. Take the square - root of both sides: $w=\sqrt{500}\approx22.4\ m$.

Answer:

$22.4\ m$