Question

I need some help here......100pts......write a quadratic equation for this problem and post a proper answer.

Answer 1

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 2

x=garden side not parallel to house

length of side parallel to house=180-2x

area=x(180-2x)=180x-2x^2

=-2(x-45)^2+4050

maximum area at x=45 equal to 4050

house side=-180-2(45)=90