Answer:
Length = 18 ft
Width = 4 ft
Step-by-step explanation:
Let the width of the rectangle be x ft
Therefore, length = (x + 14) ft
Area of rectangle = 72 sq ft
[tex] \therefore \: x(x + 14) = 72 \\ \therefore \: {x}^{2} + 14x - 72 = 0 \\\therefore \: {x}^{2} + 18x - 4x - 72 = 0 \\\therefore \: x(x + 18) - 4(x + 18) = 0 \\ \therefore \:(x + 18)(x - 4) = 0 \\ \therefore \:x + 18 = 0 \: \: or \: \: x - 4 = 0 \\ \therefore \:x = - 18 \: or \: \: x = 4 \\ \because \: dimensions \: of \: a \: rectangle \: \\ cn \: not \: be \: negative \\ \therefore \: x \neq \: - 18 \\ \implies \: x = 4 \\ \therefore \: x + 14 = 4 + 18 = 18 \\ length \: of \:the \: rectangle \: = 18 \: ft \\ width \: of \: the \: rectangle = 4 \: ft[/tex]
