1. We are asked to determine the type of triangle formed by given side lengths. 2. The classification depends on the relationship between the squares of the sides. Let the sides be $a \leq b \leq c$. 3. Use the Pythagorean theorem and its converse: - If $a^2 + b^2 = c^2$, the triangle is right. - If $a^2 + b^2 > c^2$, the triangle is acute. - If $a^2 + b^2 < c^2$, the triangle is obtuse. --- **Problem 1:** Sides 2 cm, 3 cm, 4 cm - Order: $2, 3, 4$ - Calculate squares: $2^2=4$, $3^2=9$, $4^2=16$ - Sum of smaller squares: $4 + 9 = 13$ - Compare with largest square: $13 < 16$ Since $a^2 + b^2 < c^2$, the triangle is **obtuse**. --- **Problem 2:** Sides 3.5 in, 6 in, 8.1 in - Order: $3.5, 6, 8.1$ - Squares: $3.5^2=12.25$, $6^2=36$, $8.1^2=65.61$ - Sum of smaller squares: $12.25 + 36 = 48.25$ - Compare with largest square: $48.25 < 65.61$ Since $a^2 + b^2 < c^2$, the triangle is **obtuse**. --- **Problem 3:** Sides 7, 24, 25 - Order: $7, 24, 25$ - Squares: $7^2=49$, $24^2=576$, $25^2=625$ - Sum of smaller squares: $49 + 576 = 625$ - Compare with largest square: $625 = 625$ Since $a^2 + b^2 = c^2$, the triangle is **right**. --- **Final answers:** - Problem 1: Obtuse triangle - Problem 2: Obtuse triangle - Problem 3: Right triangle