Problema Solution
A pond is inclosed by a wooden deck that is 3 ft wide. The fence surrounding the deck is 100 ft long.
a. If the pond is square, what are the dimensions?
b.If the pond is rectangular and the length of the pond is 3 times the width, what are the dimensions?
c. If the pond is circular, what is its diameter?
d. Which pond has the most area?
Answer provided by our tutors
please do not submit more than one question at a time, this four-part question is effectively four questions since each part fundamentally changes the shape of the pond and the final part switches the theme to area - please use the first answer and some tips to complete the problem
let 'x' represent the length of the pool, then 'x+3' represents the length of each side of the deck
perimeter = 2(l+w) where 'l' and 'w' are length and width, respectively
100 = 2(x+3 + x+3)
100 = 4(x+3)
25 = x+3
x = 22
if the pond is square, its dimensions are 22ft x 22ft
for a rectangular pond, let 'w' represent the width, then '3w' represents the length and we have:
100 = 2(w+3w)
50 = 4w
w = 12.5
12.5*3 = 37.5
the width would be 12.5ft, the length 37.5
if the pond is circular, then the radius would be equal to half the length of the square pool