Question

A rectangular floor has a width which is 12 feet less than the length. The perimeter of the floor is 148 feet. Set up an equation and find the length and width.

Answer 1

Length of the rectangular floor is 43 feet and width of rectangular floor is 31 feet.

Explanation:

Given:

Perimeter of rectangular floor = 148 feet

Also a rectangular floor has a width which is 12 feet less than the length.

Let the length of the rectangular floor be 'l'.

and Let the width of the rectangular floor be 'w'.

So According to question.

`w=l-12\ \ \ \ equation \ 1`

Now we know that;

Perimeter of rectangular floor is twice the sum of length and width.

framing in equation form we get;

`2(l+w)=148\\\\l+w = \frac{148}2\\\\l+w= 74 \ \ \ \ equation\ 2`

Now Substituting the equation 1 in equation 2 we get;

`l+l-12=74\\\\2l =74+12\\\\2l = 86\\\\l = (86)/(2) = 43\ ft`

Substituting the value of 'l' in equation 1 we get;

`w =l-12 = 43-12 = 31 \ ft`

Hence Length of the rectangular floor is 43 feet and width of rectangular floor is 31 feet.