Question

14. The area of a rectangle is 375 square inches and it’s perimeter is 80 inches. Find both the length and width.

Answer 1

Length
`=25` inches

Width
`= 15` inches

Explanation:

Let
`l` = length of rectangle,
`w` = width of rectangle

Given the area and the perimeter of the rectangle, we can write:

`lw = 375`

`2l+2w=80`

So:

`l+w = 80/2`

`=40`

`l=40-w`

Now, we can use substitution to find the value of
`w`:

`lw = 375`

`(40-w)w = 375`

`40w-w^2 = 375`

`375+w^2-40w = 0` (Quadratic equation)

`(w-15)(w-25) = 0`

∴
`w = 15, 25`

We can use substitution again to find the value of
`l`

`lw = 375`

`l=375/ w`

`=25,15`

∵ Length usually refers to the longer side of a rectangle, ∴ length
`=25` inches and width
`=15` inches.

Hope this helps :)