My problem is finding the greatest number of rectangular space that can be cut from 36L×60W
How big is each rectangular space?
It are the units of 36L×60W?
Yes
Sorry -- WHAT are the units of 36L * 60W?
To find the greatest number of rectangular spaces that can be cut from a given area, you need to consider the dimensions and ratios of the rectangular spaces.
In this case, you have a rectangular space with dimensions 36L × 60W. Let's assume that the length of the rectangular spaces we want to cut is L and the width is W.
To maximize the number of rectangular spaces, we need to find the largest common divisor (LCD) of the dimensions. The LCD will give us the dimensions of the largest possible rectangular spaces that can be cut from the given area.
To find the LCD, we can use the Euclidean algorithm:
Step 1: Find the remainder of dividing 60 by 36.
- Divide 60 by 36: 60 ÷ 36 = 1 remainder 24
Step 2: Replace 60 with the divisor (36) and the remainder (24).
- 36 ÷ 24 = 1 remainder 12
Step 3: Repeat step 2 until the remainder becomes zero.
- 24 ÷ 12 = 2 remainder 0
The last non-zero remainder is 12, so the LCD of 36 and 60 is 12.
Now, to find the greatest number of rectangular spaces that can be cut, we divide the dimensions of the given area by the LCD. Divide both the length and the width by 12:
Length: 36 ÷ 12 = 3
Width: 60 ÷ 12 = 5
Therefore, the greatest number of rectangular spaces that can be cut from the given area is 3 rectangular spaces with dimensions 3L × 5W.