Question

The length of a rectangle is 7cm less than 3 times it's width. It's area is 20 square cm. Find the dimensions of the rectangle

Answer 1

4 cm by 5 cm (4 x 5)

Explanation:

The area of a rectangle with length
`l` and width
`w` is given by
`A=lw`. Since the length of the rectangle is 7 less than 3 times its width, we can write the length as
`3w-7`. Therefore, substitute
`l=3w-7` into
`A=lw`:

`A=lw,\\20=(3w-7)w`

Distribute:

`20=3w^2-7w`

Subtract 20 from both sides:

`3w^2-7w-20=0`

Factor:

`(w-4)(3w+5)=0,\\\begin{cases}w-4=0, w=\boxed{4},\\3w+5=0, 3w=-5, w=\boxed{-(5)/(3)}\end{cases}`

Since
`w=-(5)/(3)` is extraneous (our dimensions cannot be negative), our answer is
`w=4`. Thus, the length must be
`20=4l, l=(20)/(4)=\boxed{5}` and the dimension of the rectangle are 4 cm by 5 cm (4 x 5).