The area of a room is 425 square feet. The length is (x+10) and the width is (x+2) feet. Find the dimensions of the room.

length = 25 feet and width = 17 feet

Step-by-step explanation:

area (A) = length * width, hence

A = (x + 10) (x + 2) ← expand factors

= x² + 12x + 20

given A = 425, then

x² + 12x + 20 = 425 (subtract 425 from both sides)

x² + 12x - 405 = 0 ← in standard form

(x + 27) (x - 15) = 0 ← in factored form

equate each factor to zero and solve for x

x + 27 = 0 ⇒ x = - 27

x - 15 = 0 ⇒ x = 15

but x > 0 ⇒ x = 15, therefore

length = 15 + 10 = 25 feet and width = 15 + 2 = 17 feet