Answer:
longest side = 7 ft
Explanation:
Area of rectangle = 28 m²
length * width = 28
(x + 3) * x =28
x*x + 3*x = 28
x² + 3x = 28
x² + 3x - 28 = 0
We look for two integers which when subtracted give 3 and when multiplied give (-28). The factors are 7 and (-4)
7 + (-4) = 3 & 7 *(-4) = -28
Rewrite the middle term using the factors.
x² + 7x - 4x -28 = 0
Take out the common factor x from the first and second term &
take out the common factor (-4) from the third and fourth term.
x(x + 7) - 4(x + 7) = 0
(x + 7) (x - 4) = 0
{Ignore x + 7 = 0 as dimensions of rectangle will not be negative}
x - 4 = 0
x = 4
x + 3 = 4 + 3
= 7
Longest side = 7 feet