SOLUTION: Jack Bauer owns a vacant lot that is 32 meters wide and 40 meters long. He makes a rectangular basketball court in the middle by subtracting equal amounts from the length and

Algebra ->  Rectangles -> SOLUTION: Jack Bauer owns a vacant lot that is 32 meters wide and 40 meters long. He makes a rectangular basketball court in the middle by subtracting equal amounts from the length and       Log On


   

Question 475597: Jack Bauer owns a vacant lot that is 32 meters wide and 40 meters
long. He makes a rectangular basketball court in the middle by
subtracting equal amounts from the length and width. The area of
the court is 560 mē. How far from the edge of the lot is an edge of
the court?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Area of lot = 32*40 = 1280 sq.m
(40-2x)(32-2x) = area of court
(40-2x)(32-2x)=560
(1280-80x-64x+4x^2)=560
1280+144x+4x^2=560
4x^2+144x+720=0
/4
x^2+36x-180=0
Find the roots of the equation by quadratic formula

a= 1 ,b= 36 ,c= -180

b^2-4ac= 1296 + 720
b^2-4ac= 2016
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=%28-12%2Bsqrt%2824%29%29%2F%2812%29
x1=( -36 + 44.9 )/ 2
x1= 4.45
x2=( -36 -44.9 ) / 2
x2= -40.45
Ignore negative value
4.45m is the width