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((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(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} (540)/(3)=(3x)/(3) \\ 180=x \end{gathered}`

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