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 pool?
a. 100 ft by 60 ft c. 55 ft by 70 ft
b. 30 ft by 40 ft d. 15 ft by 80 ft

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 pool?
a. 100 ft by 60 ft    c. 55 ft by 70 ft 
b. 30 ft by 40 ft      d. 15 ft by 80 ft

radar · Answer

$$4x ^{2}+140x=1200=4(x ^{2}+35x+300)=4(x+15)(x+20)=(2x+30)(2x+40)$$
A close look at the final results shows the total dimension (including the boardwalk) the 2x is the board walk, the dimensions of the pool are b. 30ft by 40 feet.
I guess you could of looked at the original equation for the pool and disregarded the first two terms and found out that the pond area is 1200 sq ft.  but they wanted only the dimensions of the pond.

radar · Answer

There is a typo on the first line above  change the first = to a +.

anonymous · Answer

I dont get it

radar · Answer

It is said, that "a picture is worth a 1,000 words":|dw:1402947300747:dw|