Question

3. Find the dimensions of the

Answer 1

Answer:

16 ft, 8 ft

Step-by-step explanation:

Area of rectangle = 128 Sq ft

$(x + 7)(x - 1) = 128 \\ \\ {x}^{2} - x + 7x - 7 = 128 \\ \\ {x}^{2} + 6x - 7 - 128 = 0 \\ \\ {x}^{2} + 6x - 135 = 0 \\ \\ {x}^{2} + 15x - 9x - 135 = 0 \\ \\ x(x + 15) - 9(x + 15) = 0 \\ \\ (x + 15)(x - 9) = 0 \\ \\ x + 15 = 0 \: \: or \: \: x - 9 = 0 \\ \\ x = - 15 \: or \: \: x = 9 \\ \\ \because \: side \: of \: a \: rectangle \: can \: not \: \\ be \: negative \\ \\ \implies \: x \neq - 15 \\ \\ \implies \: x = 9 \\ \\ \red{ \bold{x + 7 = 9 + 7 = 16}} \\ \\ \purple{ \bold{ x - 1 = 9 - 1 = 8}}$

Thus, the dimensions of the rectangle are 16 ft and 8 ft.