Question

The width of a rectangle is ½  its length. The perimeter of the rectangle is 540 ft. What is the length, in feet, of the rectangle? A.90 B.180 C.270 D.320

Answer 1

The width of the rectangle is half its length. Let "x" represent the length of the rectangle, then the width can be expressed as "1/2x"

The perimeter of the rectangle is calculated by adding two times its width and two times its length:

$P=2w+2l$

For the given rectangle we know that the perimeter is P=540ft, the length is l=x and the width is w=1/2x. Replace the measures in the formula:

$540=2(\frac{1}{2}x)+2(x)$

From this expression, you can determine the value of x:

-Solve the multiplications and simplify the like terms

$\begin{gathered} 540=(2\cdot\frac{1}{2})x+2x \\ 540=x+2x \\ 540=3x \end{gathered}$

-Divide both sides of the equation by 3 to determine the value of x:

$\begin{gathered} \frac{540}{3}=\frac{3x}{3} \\ 180=x \end{gathered}$

The length of the rectangle is 180ft, the correct option is B.