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There are two squares. The perimeter of the larger square is 24 cm longer than the perimeter of the smaller one, and the area of the larger square is \(80\) cm^2 more than the area of the smaller one. What is the perimeter of the smaller square in cm?

 May 23, 2022
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Let s be the length of the smaller square and r be the length of the larger square. Using this, we have the system of equations:

s^2+80=r^2

4s+24=4r

 

First, we can simplify the second equation to s+6=r, so we know that s=r-6. Plugging this in the first equation gets us

(r-6)^2+80=r^2 --> r^2-12r+116=r^2. Now we now that -12r+116=0. This gives us r=29/3 and s=11/3. Your answer is 44/3 cm.

 May 24, 2022

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