The perimeter of a rectangular room is 32m. The length of a diagonal is 8m more than than the width. Find the dimensions of the room.

12m by 4m.

Step-by-step explanation: You are looking for the dimensions of the room here, also known as the length and width.

Let’s make width equal to x since we don’t know what the value is. Length is going to be x + 8 since the diagonal is 8m MORE than the width.

w = x

l = x + 8

Use the equation for the perimeter.

P = 2l + 2w

Plug in your values:

32 = 2(x + 8) + 2(x)

Now, solve for x! First start by distributing the 2:

32 = 2x + 16 + 2x

Next, add like terms:

32 = 4x + 16

Subtract 16 from both sides:

16 = 4x

Divide by 4 on both sides:

4 = x

Now we have x, but remember, x is equal to the width. We just solved for width so now we need length.

l = x + 8

Plug in your x and solve:

l = 4 + 8

l = 12

Your length is 12m and your width is 4m, therefore, the dimensions of the rectangular room are 12m by 4m.