Question

A boardwalk that is x feet

wide is built around a rectangular pond. The

combined area of the pond and the boardwalk

is 4x^2 + 140x + 1200 square feet. What are the

dimensions of the pond?

Answer 1

4x^2 + 140x +1200
factor it out first:
2 *2(x^2 + 35x+ 300)
= 4(x+15)(x+20)
=( 2x+30) (2x+40)
After simplifying
area of the pond and sidewalk equates to:
(2x+30)(2x+40)
You know that x=sidewalk, if you want to exclude sidewalk set x = 0, to find area of only the pond
= (2(0) (30)) (2(0) + 40)
= 30 (40)
remember Area of rectangle = base times height?
Area without sidewalk = 30 times 40
so the dimensions is 30 by 40