Question

a rectangles length is three times its width, w. its area is 243 square units. which equation can be used to find the width of the rectangle?
$w^{2}=3(243)$
$3w^{2}=243$
$4w^{2}=243$
$3w^{2}=3(243)$

Explanation:

Step1: Recall rectangle - area formula

The area formula of a rectangle is $A = l\times w$, where $l$ is the length and $w$ is the width.

Step2: Express length in terms of width

Given that the length $l$ is three - times the width $w$, so $l = 3w$.

Step3: Substitute into area formula

Substitute $l = 3w$ into $A=l\times w$. We get $A=(3w)\times w$. Since $A = 243$, then $(3w)\times w=243$.

Step4: Simplify the equation

$(3w)\times w = 3w^{2}$, so the equation is $3w^{2}=243$.

Answer:

$3w^{2}=243$ (corresponding to the second option in the multiple - choice list)