The area of a room is 425 square feet. The length is (x + 11) feet and the width is (x + 3) feet. Find the dimensions of the room.

length = 25 feet

Width = 17 feet

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

The area of a room is 425 square feet. The length is (x + 11) feet and the width is (x + 3) feet. It means that

(x + 11)(x + 3) = 425

x² + 3x + 11x + 33 = 425

x² + 14x + 33 - 425 = 0

x² + 14x - 392 = 0

x² + 28x - 14x - 392 = 0

x(x + 28) - 14(x + 28) = 0

x - 14 = 0 or x + 28 = 0

x = 14 or x = - 28

The only possible value for x is 14. Hence,

Length = x + 11 = 14 + 11 = 25 feet

Width = x + 3 = 14 + 3 = 17 feet

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11