Area & perimeter puzzles
The question
A rug is a rectangle covering 24 square feet. Its braided edge runs 28 feet all the way around.
How long are its two sides?
Two facts, and only one pair fits both
area:24· perimeter:28
28÷2=14
1×24=24
2×12=24
3×8=24
4×6=24
1+24=25
2+12=14
3+8=11
4+6=10
- We know the area, 24, and the perimeter, 28, and need to work back to the sides.
- Start with the perimeter. It is two long sides and two short ones, so half of it is one of each: 28 ÷ 2 = 14. The two sides add to 14.
- Now use the area to write out the possibilities. These are all the ways two whole numbers multiply to 24 — 4 of them.
- So go down the list adding each pair, and stop where the total is 14: 2 + 12 = 14. That is the only pair that fits both facts.
How it works.
- 01
We know the area, 24, and the perimeter, 28, and need to work back to the sides.
- 02
Start with the perimeter. It is two long sides and two short ones, so half of it is one of each: 28 ÷ 2 = 14. The two sides add to 14.
- 03
Now use the area to write out the possibilities. These are all the ways two whole numbers multiply to 24 — 4 of them.
- 04
So go down the list adding each pair, and stop where the total is 14: 2 + 12 = 14. That is the only pair that fits both facts.