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A rectangular room is 1.8 times as long as it is wide, and its perimeter is 29 meters. Find the dimension of the room. The length is : meters and the width is meters.

User Triode
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Dimensions of a room

Step 1: finding an expression for each side of the rectagle

Let's say x is going to be the number meters of the width of the room:

x: width

Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:

1.8x: lenght

Step 2: relating the expressions for each side to its perimeter

We know that the perimeter of a rectangle is given by

Perimeter = 2· (width + lenght)

We know that the perimeter is 29 meters, then

Perimeter = 29

29 = 2· (width + lenght)

We do know an expression for its width and lenght, we replace them:

29 = 2· (width + lenght)

29 = 2· (x + 1.8x)

Step 3: finding x

Since x + 1.8x = 2.8x:

29 = 2· (x + 1.8x)

29 = 2· (2.8x)

↓ 2· 2.8 = 5.6

29 = 5.6x

↓ dividing both sides by 5.6

29/5.6 = 5.6x/5.6

5.2 = x

Final step: finding its dimensions

Since

x: width

then

Width = 5.2 meters

Since

1.8x: lenght

then

Lenght = 1.8 · 5.2 meters = 9.36 meters

Answer: the dimensions of the room are Width = 5.2 meters and Lenght = 9.36 meters

User Watbywbarif
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