# The length of a room is 4 times longer than it's width. its area is { 36 m^2 }. Find the...

## Question:

The length of a room is 4 times longer than it's width. its area is {eq}36 m^2 {/eq}. Find the dimensions of the room?

## Dimensions of a Rectangle; System of Equations:

{eq}\\ {/eq}

Here we have given a room (rectangle type construction) and we have to determine its dimensions (length and width). First of all, we will convert the given statements in terms of two algebraic equations then we will solve them using the method of substitution. Then finally, we will get the values of the length and width in the meter.

{eq}\\ {/eq}

Let us assume:

The length of the room is {eq}\; = \text {L} \; \text {m} {/eq}

The width of the room is {eq}\; = \text {W} \; \text {m} {/eq}

We have given that the length of the room is 4 times longer than its width so:

{eq}\text {L} = 4 \times \text {W} \; \; \cdots \cdots \; \; (1) {/eq}

The area of the room is {eq}\; = \text {L} \times \text {W} = 36 \; \text {m}^{2} \; \; \cdots \cdots \; \; (2) {/eq}

Now using equation (1) and (2), we get the following:

{eq}\biggr(4 \text {W} \biggr) \times \text {W} = 36 \\ 4 \text {W}^{2} = 36 \\ \text {W}^{2} = \dfrac {36}{4} \\ \Longrightarrow \text {W} = 3 \; \text {m} {/eq}

Now put the value of {eq}\text {W} = 3 {/eq} in equation (1) in order to get the value of {eq}\text {L} {/eq}:

{eq}\Longrightarrow \text {L} = 4 \times 3 = 12 \; \text {m} {/eq}

Finally, we have the dimensions of the room as given below:

{eq}\Longrightarrow \boxed {(\text {L}, \; \text {W}) = (12 \; \text {m}, \; 3 \; \text {m})} {/eq}