Question

The length of a rectangle is 4 meters longer than its width.

The area of the rectangle is 192m^2.
What is the width of the rectangle?
HINT: you can use DESMOS for this kind of problem.

Answer 1

Answer: width is 12 m

Explanation:

Let
`x` be the length of the rectangle. Then the width is
`x-4.` The area of a rectangle is base times height, so our variable
`x` satisfies the equation:

`x(x-4)=192.`

After a bit of algebraic manipulation, we get
`x^2-4x-192=0,` and we can solve this using the quadratic formula.

This gives us
`x = (4 \pm √(16+4*192))/(2) = (4 \pm 28)/(2) = 2 \pm 14.` However, we must take the positive solution, as lengths in geometry are always positive. Hence,
`x = 2+14=16,` and width is just
`x-4` which is equal to
`\boxed{12}`.