Question

The edges of three squares are joined together to form a right triangle with legs of lengths r and s and a hypotenuse of length t. What must be true?

Answer 1

Answer: Choice A

The area of square T is equal to the sum of the areas of square R and square S.

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Explanation:

Recall that the pythagorean theorem says

a^2+b^2 = c^2

Visually this means if we had a square with side length 'a', then its area is a^2. The same goes for a square with side length b. Its area is b^2

So a^2+b^2 is the sum of those square areas. It being equal to c^2 tells us that adding the smaller square areas lead to the largest square area.

So that's why the areas of squares R and S add up to the area of square T.

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An example:

Let's say...

• square R has side length 3
• square S has side length 4
• square T has side length 5

note how 3^2+4^2 = 9+16 = 25 and how 5^2 = 25. This shows 3^2+4^2 = 5^2