1. **State the problem:** We are given four models, each with three squares attached to a triangle. The areas of the squares are given, and we need to determine which model can be used to prove the triangle is a right triangle using the Pythagorean Theorem. 2. **Recall the Pythagorean Theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the areas of the squares on the sides satisfy: $$a^2 + b^2 = c^2$$ 3. **Identify the squares' side lengths:** Since the areas of the squares are given, the side lengths of the squares (which correspond to the triangle's sides) are the square roots of the areas. 4. **Check each model:** - Model A: Areas = 14, 25, 8 - Side lengths: $\sqrt{14}$, $\sqrt{25} = 5$, $\sqrt{8}$ - Check if $\sqrt{14}^2 + \sqrt{8}^2 = 5^2$? - $14 + 8 = 22 \neq 25$ - Model B: Areas = 38, 50, 12 - Side lengths: $\sqrt{38}$, $\sqrt{50}$, $\sqrt{12}$ - Check sums: - $38 + 12 = 50$? - $50 = 50$ (True) - So, $\sqrt{38}^2 + \sqrt{12}^2 = \sqrt{50}^2$ - Model C: Areas = 144, 169, 25 - Side lengths: $12$, $13$, $5$ - Check if $12^2 + 5^2 = 13^2$? - $144 + 25 = 169$ - $169 = 169$ (True) - Model D: Areas = 20, 25, 15 - Side lengths: $\sqrt{20}$, $5$, $\sqrt{15}$ - Check sums: - $20 + 15 = 35 \neq 25$ 5. **Conclusion:** Models B and C satisfy the Pythagorean Theorem condition. However, Model C corresponds to the well-known Pythagorean triple $(5,12,13)$ scaled differently, but here the sides are $5$, $12$, and $13$ (since $\sqrt{25} = 5$, $\sqrt{144} = 12$, $\sqrt{169} = 13$). Model B's sides are irrational and less common but also satisfy the theorem. Since the problem asks which model can be used to prove the triangle is right by the Pythagorean Theorem, Model C is the clearest and most standard example. **Final answer:** Model C