Question

A rectangle room is three times as long as it is wide and it perimeter is 56 m find the width of the room

Answer 1

\[3l=w \]

Answer 2

l represents length and w represents width. Therefore, the length w is 3 times bigger than the length. The equation for perimeter is \[P=2l+2w\]

Answer 3

Now just plug in the value for w in terms of l and it looks like this:
\[P = 2l+2(3l)\]

Answer 4

Now remember that the given perimeter was 56m so setting P = 56 m, you get:
\[56 = 2l+6l\]

Answer 5

now solve for l which is \[56 = 8l \rightarrow l=56/8\rightarrow 7\]

Answer 6

you know that 3 times the length is the width, therefore, knowing the length, 3 times 7 is 21 and 21 is the width of the rectangle.