Question 23
A rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters. Find the dimension of
the room.
The length is:
Check Answer

Question

Question 23 A rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters. Find the dimension of the room. The length is: Check Answer

UpStudy AI · Accepted Answer

Let the width of the room be $$ w $$ meters. Then the length is given by  
$$
w + 6
$$
since the room is 6 meters longer than it is wide.

The perimeter $$ P $$ of the rectangular room is given by the formula  
$$
P = 2(\text{length} + \text{width})
$$
We know that $$ P = 36 $$ meters, so we have  
$$
2\left(w + (w + 6)\right) = 36
$$

Now, simplify inside the parentheses:
$$
w + (w + 6) = 2w + 6
$$

So the equation becomes:
$$
2(2w + 6) = 36
$$

Divide both sides of the equation by 2:
$$
2w + 6 = 18
$$

Subtract 6 from both sides:
$$
2w = 12
$$

Divide both sides by 2:
$$
w = 6
$$

Now that we have the width, the length is:
$$
w + 6 = 6 + 6 = 12
$$

Thus, the length of the room is  
$$
\boxed{12 \text{ meters}}
$$
The length of the room is 12 meters.

Question 23
A rectangular room is 6 meters longer than it is wide, and its perimeter is 36 meters. Find the dimension of
the room.
The length is:
Check Answer

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