Answer:
length = 3 meters and width = 2 meters
length = 2 meters and width = 3 meters
Explanation:
If you want to find out how big a rectangle is when you know its perimeter and area, you can use some math tricks. Here are the tricks:
Perimeter of a rectangle = 2 times (length plus width) 1
Area of a rectangle = length times width 2
Now we can use these tricks to find the length and width of the rectangle. Let's say the length is l and the width is w. Then we can write:
2 times (l plus w) = 10
l times w = 6
We can make the first trick easier by cutting both sides in half:
l plus w = 5
We can then get rid of one letter by using the other one. For example, we can write l as 5 minus w:
l = 5 - w
Then we can put this into the second trick:
(5 - w) times w = 6
This makes a puzzle that we can solve by opening up, moving around, and grouping:
5w minus w squared = 6
w squared minus 5w plus 6 = 0
(w minus 2) times (w minus 3) = 0
This means that either w minus 2 = 0 or w minus 3 = 0. Solving for w, we get two answers:
w = 2 or w = 3
We can then use these answers to find the matching answers for l:
If w = 2, then l = 5 - w = 5 - 2 = 3
If w = 3, then l = 5 - w = 5 - 3 = 2
So we have two ways to make the rectangle:
length = 3 meters and width = 2 meters
length = 2 meters and width = 3 meters