A rectangular park is three blocks longer than it is wide. the area of the park is 40 square blocks. If w represents the widths, write an equation in terms of w for the area of the park. Find the length and width of the park.
Hello,
let l be the length of the park
let w be the width of the park
Then you know: l = w + 3
and a = l * w
Plug in the term for l :
$\displaystyle a(w) = w \cdot (w+3) = w^2 + 3w$
You know: a = 40
Now you have a quadratic equation to solve:
$\displaystyle w^2 + 3w = 40 \Longleftrightarrow w = 5 \vee a = -8$
The negative solution isn't very plausible here. Thus the park is 8 blocks long and 5 blocks wide.