Question

Three square grids, D, E, and ?, connect at their vertices to form a right triangle. Square grid D is 65 squares across and square grid E is 97 squares across. How many total squares are in grid F?

a. 32
b. 162
c. 5,184
d. 13,634

Answer 1

To find the total number of squares in grid F, you need to add up the number of squares in grids D and E, and then subtract the number of overlapping squares.

Step-by-step explanation:

To find the total number of squares in grid F, we need to add up the number of squares in grids D and E, and then subtract the number of overlapping squares. Grid D is 65 squares across, so it has a total of 65^2 = 4225 squares. Grid E is 97 squares across, so it has a total of 97^2 = 9409 squares. The overlapping region will have squares with sides equal to the difference between the widths of the two grids, so it will have (97-65)^2 = 3844 squares. Therefore, the total number of squares in grid F is 4225 + 9409 - 3844 = 9790 squares.