So I have to draw two rectangles on graph paper that each have to fit in a 15 by 20 block. The first rectangle can be what ever size you want but the second one needs be similar with a 3/5 ratio of the first. I can't figure out what their sizes should be.
1. Choose Length and Width of the larger rectangle that are divisible by 5.
2. The corresponding sides of the smaller rectangle should be 3/5 of the larger.
L1 = 10
W1 = 5
L2 = (3/5) * 10 = 6.
W2 = (3/5) * 5 = 3.
To determine the sizes of the two rectangles, let's break down the problem step by step.
Step 1: Determine the size of the first rectangle.
Since the first rectangle can be any size, we can start by choosing dimensions that are easy to work with. Let's say the first rectangle has a width of 5 blocks. Now we need to determine its height.
Step 2: Calculate the height of the first rectangle.
To find the height, we need to consider the 3/5 ratio mentioned for the second rectangle. This means that the second rectangle's height will be 3/5 of the first rectangle's height. To simplify calculations, let's assume the height of the first rectangle is 5 blocks. Applying the 3/5 ratio, the height of the second rectangle will be (3/5) * 5 = 3 blocks.
Step 3: Verify if the rectangles fit in a 15 by 20 block area.
Now we need to check if the two rectangles fit within the 15 by 20 block area.
For the first rectangle:
Width = 5 blocks
Height = 5 blocks
The area of the first rectangle is 5 * 5 = 25 square blocks.
For the second rectangle:
Width = (3/5) * 5 = 3 blocks
Height = 3 blocks
The area of the second rectangle is 3 * 3 = 9 square blocks.
To check if they both fit within the 15 by 20 block area, we sum their areas:
25 + 9 = 34 square blocks.
Since 34 square blocks is less than the area of the 15 by 20 block area (300 square blocks), both rectangles will fit.
Thus, the sizes of the two rectangles can be a width of 5 blocks and a height of 5 blocks for the first rectangle, and a width of 3 blocks and a height of 3 blocks for the second rectangle.