the area of a room is 96 square feet. The length is (x+1) feet and the width is (x-3) feet. find the dimensions of the room

length = 12 feet and width = 8 feet

Step-by-step explanation:

since the area = 96 ft² then

(x + 1) (x - 3) = 96 (A = lw)

expand the factors on the left side

x² - 2x - 3 = 96 (subtract 96 from both sides)

x² - 2x - 99 = 0 ← in standard form

(x - 11) (x + 9) = 0 ← in factored form

equate each factor to zero and solve for x

x - 11 = 0 ⇒ x = 11

x + 9 = 0 ⇒ x = - 9

but x > 0 ⇒ x = 11

length = 11 + 1 = 12 feet and width = 11 - 3 = 8 feet