Question

One side of a rectangle is 20cm longer than another side. If you double the length of the shorter side and triple the length of the longer side, then the perimeter of the new rectangle will be 240cm. Find the lengths of the sides of the original rectangle.

Answer 1

The length of the short side was 12 and the length of the long side was 32

Explanation:

We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:

w = l + 20

And

2(2l + 3w) = 240

We will start with the second equation, then substitute in the first equation for w. We have:

4l + 6w = 240

Divide both sides by 2:

2l + 3w = 120

Then, we substitute in l + 20 for w, giving us:

2l + 3l + 60 = 120

Subtract 60 from both sides and combine like terms:

5l = 60

l = 12

So, the original length was 12, now substituting this into our first equation gives us:

w = 12 + 20 = 32

So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.

Hope this helped!