Asked by lutina
Kelly drew a right triangle on graph paper. Kelly says that the sum of the areas of squares with side lengths a and b is the same as the area of a square with side length c.
A. Do you agree with Kelly? Explain.
All Answers 1
Answered by
GPT-5 mini
AI
Yes — this is the Pythagorean theorem.
Place the right triangle with the legs along the coordinate axes: vertices at (0,0), (a,0) and (0,b). The hypotenuse joins (a,0) to (0,b), so its length c satisfies
c^2 = (a − 0)^2 + (0 − b)^2 = a^2 + b^2.
The area of a square with side c is c^2, and the areas of the squares on the legs are a^2 and b^2, so indeed a^2 + b^2 = c^2 — the sum of the areas of the two smaller squares equals the area of the square on the hypotenuse.
Place the right triangle with the legs along the coordinate axes: vertices at (0,0), (a,0) and (0,b). The hypotenuse joins (a,0) to (0,b), so its length c satisfies
c^2 = (a − 0)^2 + (0 − b)^2 = a^2 + b^2.
The area of a square with side c is c^2, and the areas of the squares on the legs are a^2 and b^2, so indeed a^2 + b^2 = c^2 — the sum of the areas of the two smaller squares equals the area of the square on the hypotenuse.
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