Question

A triangle formed by three squares joined at their vertices. The side lengths of the squares are 2, 3 1/3, and 2 2/3. Is the triangle a right triangle?
A. Yes, because the areas of the two smaller squares add up to the area of the largest square.

B. Yes, because any triangle formed by three squares joined at their vertices will be a right triangle.

C. No, because 2 + 2 2/3 $\neq$ 3 1/3

D. No, because 4 - 100/9 $\neq$ 64/9

Answer 1

If it is a right triangle, then this must be true:

$(2)^2 + (2\frac{2}{3})^2 = (3\frac{1}{3})^2$

$(2)^2 + (\frac{8}{3})^2 = (\frac{10}{3})^2\\\\4 + \frac{64}{9} = \frac{100}{9}\\\\\frac{36}{9} +\frac{64}{9} =\frac{100}{9}\\\\\frac{100}{9}=\frac{100}{9}$

The correct answer is: A. Yes, because the areas of the two smaller squares add up to the area of the largest square.