let x be the two sides 90deg to the house
house side = 180-2x
Draw a rectangle with length of 2 sides at right angle to house=x
Length of side parallel to house=180-2x
Garden area=x(180-2x)
=180x-2x^2
=-2x^2+180 x
complete the square:
=-2(x^2-90x)
=-2(x^2-90x+2025)+4050
=-2(x-45)^2+4050
so area is max at x-45=0
x=45
House side=180-2*45=90
Garden with the greatest area: 45 by 90 ft
Greatest area=45*90=4050 sq ft
Answer:
Step-by-step explanation:
wall as one side so only 3 sides of fence
let x n y be width n length of garden
length of garden fence = y + 2x
area of garden = x*y
given y + 2x = 180
y = 180 - 2x
substitute into area
area = (180 - 2x)*x = 180x - 2x*x
= 180x - 2x^2
tis the ans 4 quadratic equation
to find max area, use differentiation
d(180x - 2x^2)/dx = 0
180 - 4x = 0
x = 45
y = 180 - 2(45)
= 90
greatest area = 45*90 = 4050 sq ft
