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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?

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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



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