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The diagrams below show Alvin's and Simon’s bedrooms. If the perimeter of each of their bedrooms is the same, what is the length and width of Alvin’s bedroom?

The diagrams below show Alvin's and Simon’s bedrooms. If the perimeter of each of-example-1
User Shender
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1 Answer

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Answer:

length = 40 ft, width = 15 ft

Explanation:

Since both rooms are rectangles, we know each side is the same as it's opposing side. So:

Alvin's bedroom perimeter = x+(x-25)+x+(x-25), which can be simplified to 4x+50

Simon's bedroom perimeter = (x+10)+2x+(x+10)+2x+(x+10), which can be simplified to 6x+20

Because the perimeters of the bedrooms are the same, we can set the equations equal to each other. So: 4x+50=6x+20

Then you solve the equation.

4x+50=6x+20

4x+(50-20)=6x(20-20)

4x+30=6x

(4x-4x)+30=(6x-4x)

30=2x

30/2=2x/2

15=x

Now that we know 15 = x, we can plug that in to the original length and width of Alvin's Bedroom:

Length = (x+25) = (15+25) ft = 40 ft

Width = x ft = 15 ft

Therefore, the length of Alvin's bedroom is 40 feet and the width of his bedroom is 15 feet.

User Solopiu
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