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.