A right triangle is shown in the diagram below.
A triangle has a grid of 8 rows of squares with 8 squares in each row below its base and a grid of 6 rows of squares with 6 squares in each row along its height and a square along the hypotenuse of the triangle.
Based on the Pythagorean Theorem, which statement is correct?
A.
The empty square has a side length of 8 and an area of 64 square units.
B.
The empty square has a side length of 9.6 and an area of 92 square units.
C.
The empty square has a side length of 10 and an area of 100 square units.
D.
The empty square has a side length of 14 and an area of 196 square units.
C. The empty square has a side length of 10 and an area of 100 square units.
Using the Pythagorean Theorem:
a^2 + b^2 = c^2
8^2 + 6^2 = c^2
64 + 36 = c^2
100 = c^2
c = 10
Therefore, the side length of the empty square is 10 units and the area is 100 square units.