I am a third grader and have a homework of sketching and labeling all possible rectangles with perimeter of 30 cm and sides whose lengths are whole numbers. I am confuse, i need help please.
The formula for perimeter is,
P = 2w + 2 L
30 = 2w + 2L
30 = 2(w + l)
15 = w + l
So, for a perimeter of 30, you want to sketch rectangles that the width and length total 15.
Some possible rectangles,
14 + 1 = 15
13 + 2 = 15
12 + 3 = 15
11 + 4 = 15
10 + 5 = 15
9 + 6 = 15
8 + 7 = 15
Do you follow what I am doing?
I gave you a good start. Find the remaining sides that when added, equal 15.
Good luck! :)
I will try. This will help me to start and gave me an idea. Thank you very much.
You're welcome.
Sure, I can help you with that! To sketch and label all possible rectangles with a perimeter of 30 cm and sides whose lengths are whole numbers, we first need to understand what perimeter means. The perimeter is the distance around the outside of a shape. For a rectangle, it is the sum of all its sides.
To start, let's think about the possible lengths for each side of the rectangle. We know that the lengths should be whole numbers, so we have to find pairs of numbers that add up to 15 (since the perimeter is 30 cm).
We can start by considering the smallest possible side length, which is 1 cm. In this case, we need to find pairs of numbers that add up to 15 - 1 = 14 (because we have already used one for the first side).
Here are all the possible pairs of whole numbers that add up to 14:
- 1 cm and 13 cm
- 2 cm and 12 cm
- 3 cm and 11 cm
- 4 cm and 10 cm
- 5 cm and 9 cm
- 6 cm and 8 cm
- 7 cm and 7 cm
Now, we can draw rectangles using these pairs of numbers. To sketch a rectangle, draw two parallel lines (long sides) and two perpendicular lines (short sides) connecting the ends of the parallel lines. The length of one side of the rectangle would be one number from the pair, and the length of the other side would be the other number from the pair.
For example, if we take the pair 1 cm and 13 cm, we can draw a rectangle where one side measures 1 cm and the other side measures 13 cm. Label the sides with their lengths.
Repeat this process with each pair of numbers to sketch and label all possible rectangles with a perimeter of 30 cm and whole number side lengths.
Remember to double-check your work and make sure you didn't miss any pairs or possible rectangles. It's always a good idea to show your work neatly and clearly on paper, so your teacher can understand your thinking.
I hope this explanation helps! Let me know if you have any further questions.