# Length of a Room - Word problems

A rectangular room is 14 feet narrower than its length. If 392 square feet of carpet is needed to cover the entire room, what is the length of the room?

### Comments for Length of a Room - Word problems

 Apr 20, 2012 Length of a Room by: Staff Question: A rectangular room is 14 feet narrower than its length. If 392 square feet of carpet is needed to cover the entire room, what is the length of the room? Answer: A = area of room L = length of room W = width of room The equation for the area of the room is: A = L * W area of the room is 392 square feet A = 392 ft² 392 = L * W L * W = 392 A rectangular room is 14 feet narrower than its length W = L - 14 You now have two equations with two unknowns: 1st equation: L * W = 392 2nd equation: W = L - 14 Solve for L Substitute L - 14 for W in the 1st equation L * W = 392 L * (L - 14) = 392 Eliminate the parentheses using the distributive law L * (L - 14) = 392 L * L - 14 * L = 392 L² - 14L = 392 Subtract 392 from each side of the equation L² - 14L - 392 = 392 - 392 L² - 14L - 392 = 0 The result is a quadratic equation of the form: ax² + bx + c = 0 L² - 14L - 392 = 0 The length (L) can be easily determined by factoring the equation L² - 14L - 392 = 0 (L + 14)*(L - 28) = 0 (L + 14) = 0 L + 14 = 0 L + 14 - 14 = 0 - 14 L + 0 = 0 - 14 L₁ = -14 (L - 28) = 0 L - 28 = 0 L - 28 + 28 = 0 + 28 L + 0 = 0 + 28 L₂ = 28 There are two solutions to the equation: L₁ = -14 L₂ = 28 However, the length of the room can only be a positive value. Therefore, the length is: L₂ = 28 feet To determine the width of the room, substitute 28 for the length of the room in equation 2: W = L - 14 W = 28 - 14 W = 14 feet >>> the final answer is: W = 14 feet L = 28 feet Thanks for writing. Staff www.solving-math-problems.com