Calculate Rectangle Dimensions: From 8cm × 12cm to 200cm Perimeter

Question

Imagine two identical rectangles.

The lengths of the first rectangle's sides are 8 cm and 12 cm, while the perimeter of the second rectangle is 200 cm.

What are the lengths of the second rectangle's sides?

Video Solution

Solution Steps

00:13 Let's find the lengths of the second rectangle's sides.
00:16 First, we'll label one side as X. This helps us keep track.
00:21 Now, we need to find the similarity ratio. This ratio compares the two rectangles.
00:27 The similarity ratio is the same as the ratio of their perimeters.
00:32 Remember, the perimeter is the sum of all the sides around a rectangle.
00:41 Let's substitute the given values into the formula and solve for X.
00:55 We'll factor 200 into 40 and 5, then simplify.
01:01 Next, multiply by the reciprocal to isolate X.
01:09 Great! Now, we have the length of side X.
01:17 Let's mark the other side as Y. Ready to solve for this too.
01:21 Just like before, the perimeter is the total of all sides.
01:28 We'll gather all terms together.
01:34 Now, let's isolate Y to find its length.
01:41 And there you have it. That's how we solve for both sides of the rectangle!

Answer

60 cm and 40 cm