Question

The perimeter of a rectangle is 176 feet. The ratio of the width to the length is 3:5. Find the area of the rectangle.

Answer 1

Answer:

Area of the rectangle = $1815\,feet^2$

Step-by-step explanation:

Perimeter of the rectangle= $176\,feet$

Ratio of the width to length is :

$\dfrac{W}{L} =\dfrac{3}{5}$

Therefore ,

                  $L=\dfrac{5W}{3}$

Perimeter of a rectangle= $2(Length+Width)$

     $176=2(\dfrac{5W}{3}+W )\\\\\dfrac{176}{2} = \dfrac{5W}{3}+W \\\\88=\dfrac{5W+3W}{3} \\\\ 88=\dfrac{8W}{3}\\\\ \dfrac{W}{3}=\dfrac{88}{8}\\\\ \dfrac{W}{3}=11\\\\ W=11\times3\\\\W=33\,feet$

As.

  $L=\dfrac{5W}{3}$

$L=\dfrac{5\times33}{3} \\\\L=55\,feet$

Area of a rectangle= $Length\times Width$

                     $=55\times33\\\\=1815\,feet^2$

Area of the rectangle = $1815\,feet^2$