The area of a rectangular pool is given by the equation A=w^2+10w, where W is the width of one side. A) Write an expression for the length of the pool, L= B) If the area of the pool is 600 square feet, find the dimensions.

# A rectangle A= w^2 + 10w, where W is the width of oneside, expression for length? A=600, dimensions?

- Posted:
- 3+ months ago by Bigbacca21
- Topics:
- expression, area, write, math, equations, help, dimension, length

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## Answers (1)

A)

A = w^2 + 10w

A = w (w + 10)

l = w + 10

B)

w^2 + 10w = 600

w^2 + 10x - 600 = 0

Solve this nice quadratic with the formula

x1 = -p/2 - sqrt( p^2 /4 - q )

x2 = -p/2 + sqrt( p^2 /4 - q )

and p = 10 ; coefficient of the linear term

and q = - 600

x1 = - 30

x2 = 20

x1 goes away, as negative lengths don't make much sense, and we just take

w = x2 = 20 and get:

l = w + 10 = 30

Plug these values in:

A = w^2 + 10w

A= 20^2 ft^2 + 10ft * 20ft

A= 400ft^2 + 200ft^2

A = 600ft^2

or

A = w (w + 10) = w * l

A = 20ft (20ft + 10ft)

A = 20ft * 30ft = 600ft^2