how many rectangles can be formed by a 10x10 square and a 7x8 rectangle? Squares are classified as rectangles

Chickenisyummywith Mar 22, 2023

#2**+1 **

To count the number of rectangles that can be formed by a 10x10 square and a 7x8 rectangle, we can use the formula:

Number of rectangles = (number of horizontal lines choose 2) x (number of vertical lines choose 2)

For the 10x10 square, there are 11 horizontal lines and 11 vertical lines, so we get:

Number of rectangles in the 10x10 square = (11 choose 2) x (11 choose 2) = 55 x 55 = 3,025

For the 7x8 rectangle, there are 8 horizontal lines and 9 vertical lines, so we get:

Number of rectangles in the 7x8 rectangle = (8 choose 2) x (9 choose 2) = 28 x 36 = 1,008

Now, we can add the number of rectangles in the 10x10 square and the 7x8 rectangle to get the total number of rectangles:

**Total number of rectangles = 3,025 + 1,008 = 4,033**

**Therefore, there are 4,033 rectangles that can be formed by a 10x10 square and a 7x8 rectangle.**

Guest Mar 22, 2023