Pre cal math about solving geometry word problem

Question

the length of a rectangular swimming pool is 20 feet greater than its width. the surface area of the pool is 1500 square feet. What is the length and width of the pool?

Answer 1

the length of a rectangular swimming pool is 20 feet greater than its width. the surface area of the pool is 1500 square feet. What is the length and width of the pool?

Let L = length

W = width

Important formulas:

Area = L * W

Fill in the given information:

L = W + 20

A = L * W

1500 = (W+20) * W

1500 = W^2 + 20W [expand]

W^2 + 20W - 1500 = 0 [get all on left side]

(W - 30)(W + 50) = 0 [either factor or use quadratic formula]

Either W = 30 or W = -50 or both {Multiplicative Property of Zero]

NOTE: W cannot be -50, so W=30

L = W + 20

L = 50



The pool is 50 ft by 30 ft.

Answer 2

Let x = width of the pool

x+20 = length of the pool

Area = length x width

Plugging everything into the formula

1500=x(x+20) Distributive property

1500=x²+20x Subtract 1500 from both sides to set equal to 0

1500-1500=x²+20x-1500

0=x²+20x-1500 Factor

0=(x-30)(x+50) Set factors equal to zero and solve

x-30=0

x=30

x+50=0

x=-50 x cannot be negative for a pool dimension

The width of the pool is 30 ft. The length is 50 ft. (30+20 using the equation set up above)