middddtermmms help

Question

A rectangular room is twice as long as it is wide, and its perimeter is 48 meters. Find the width of the room. 

Answer 1

Hi Kris,

First, we need to assign some expressions to the length and width of this rectangular room. Therefore:

Let x equal the room's width

Let 2x equal the room's length

Second, we need to use the formula for determining the perimeter of a rectangle since this room is rectangular.

The formula is P = 2(L + W) or P = 2(L) + 2(W) where P equals the perimeter, L equals the length, and W equals the width. Please notice that the second formula is exactly the same as the first one with one exception which is we applied the distributive property of mathematics. Now, we substitute our expressions.

P = 2(2x) + 2(x)

48 = 4x + 2x

48 = 6x

x = 8 meters <------This is the room's width

2x = 2(8) = 16 meters <-----_This is the room's length

Finally we want to check our work. And when we do that we use the formula substituting both numbers for the L and W.

P = 2(16) + 2(8)

48 = 32 + 16

48 = 48

Therefore, the width of the room is 8 meters wide. I hope this helps. Good luck on your mid-terms. Best!