SOLUTION: Ms. S. has a rectangular flower garden that measures 15 by 20 meters. She wishes to build a concrete walk of uniform width around the garden. Her budget for the project allows her

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Ms. S. has a rectangular flower garden that measures 15 by 20 meters. She wishes to build a concrete walk of uniform width around the garden. Her budget for the project allows her       Log On


   

Question 725483: Ms. S. has a rectangular flower garden that measures 15 by 20 meters. She wishes to build a concrete walk of uniform width around the garden. Her budget for the project allows her to buy enough concrete to cover an area of 74 square meters. How wide can she build the walk?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Length of garden 15 m
width of garden 20 m

Area = 300 m^2
Area of sidewalk 72 m^2
length of garden & sidewalk 15 + 2 x
width of garden & sidewalk 20 + 2 x

( 15 + 2 x ) ( 20 + 2 x ) + -300 = 72

300 + 30 x + 40 x + 4 X^2 + -300 = 72
4 X^2 + 70 x + -72 = 0
Find the roots of the equation by quadratic formula
a= 4 b= 70 c= -72
b^2-4ac= 4900 - -1152
b^2-4ac= 6052 sqrt%28%096052%09%29= 77.79
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -70 + 77.79 )/ 8
x1= 0.97
x2=( -70 -77.79 ) / 8
x2= -15.5
Ignore negative value
width of sidewalk = 0.97 m