Given:
A = 18 ft²
formula for the area of a rectangle is:
length x width
lets use:
A = l x w
solution by trial and error.
so the area must be 18 ft²
let l be any real number greater than 0 but less than or equal to 18
0 < l ≤ 18
assume any value of l greater than 0 but less than or equal to 18
like l = 3ft
A = 3 x w
18 = 3 x w
w = 6ft
or l = 4ft
18 = 4 x w
w = 4.5 ft
check
A = l x w
for l = 3
A = 3 x 6
A = 18 ft²
for l = 4
A = 4 x 4.5
A = 18 ft²
3.)
let w = l+7
A = l x w
by substitution
18 = l x ( l + 7)
18 = 2l² + 7l
l = 2 ft
w = l + 7
w = 2 + 7
w = 9 ft
check
18 = 9 x 2
18 = 18
4.
18 = 2l² + 7l
2l² + 7l -18 = 0 is a quadratic equation