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