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Length (L) equals 4 x Width (W)

Area (A) is equal to L x W and is equal to 16m2

We have two equations

(1) L = 4W

(2) A = L x W

Since we know A = 16 (m2) we have two unknowns (L and W)

Algebraic substitution of equation (1) into equation (2) gives us

(3) A = 4W x W

replacing 16m2 for A

(4) 16 = 4W x W

Simplification

(5) 16 = 4 W^2

(6) 16/4 = W^2

(7) 4 = W^2

Take the square root

(8) 2 = W

using the solution for W in equation (1)

(9) L = 4 x W

(10) L = 4 x 2

(11) L = 8

Check work using equation (2)

A = L x W

A = 8 x 2

A = 16

Improved answer:

Let the unknown length and width be 4x and x respectively:

4x*x = 16

4x2 = 16. Divide both sides by 4:

x2 = 4. Square root both sides:

x = 2

Therefore: length = 8 meters and width = 2 meters

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Q: Larry wants to buy some carpeting for his living room the length of the room is 4 times the width and the total area of the room is 16 square meters what is the length of the living room?
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