Question

Suppose that the width of a certain rectangle is 1 inch more than one-fourth of its length. The perimeter of the rectangle is 62 inches. Find the length and width of the rectangle.

Answer 1

The length of the rectangle is 24 inches and the width is 7 inches

Explanation:

Let

x ----> the length of rectangle

y ----> the width of rectangle

we know that

The perimeter of rectangle is equal to

`P=2(x+y)`

we have

`P=62\ in`

so

`62=2(x+y)`

`31=x+y` ----> equation A

`y=(1)/(4)x+1` ---> equation B

Solve the system by substitution

substitute equation B in equation A

`31=x+(1)/(4)x+1`

solve for x

`(5)/(4)x=30`

`x=30(4)/5\\x=24`

Find the value of y

`y=(1)/(4)(24)+1\\\\y=7`

therefore

The length of the rectangle is 24 inches and the width is 7 inches