Question

The area of a children's rectangular playground is 1189 square meters. The length

is 12 meters longer than the width. Determine the length and width of the
playground.

Answer 1

`1+√(1190)` and
`√(1190)-11`

Explanation:

Let the length in meters be
`l`. Then, the width is
`l-12`.

`l(l-12)=1189 \\ \\ l^2-12l=1189 \\ \\ l^2-2l-1189=0 \\ \\ l=(2 +√((-2)^2-4(1)(-1189)))/(2(1)) \text{ } (l>0) \\ \\ l=1+√(1190) \\ \\ \implies l-12=√(1190)-11`