lengths of two triangles are given below. the questions about each triangle. Compute the sum of the squares of the shorter lengths. \[ 9^{2}+13^{2}= \] \( \square \) Compute the square of the longest length. \[ 14^{2}= \] \( \square \) What kind of triangle is it? Acute triangle Right triangle Ottuse triangle (b) The other triangle has side lengths 24,26 , and 10 . Compute the sum of the squares of the shorter lengths. \[ 10^{2}+24^{2}= \] \( \square \) Compute the square of the longest length. \[ 26^{2}= \] \( \square \) What kind of triangle is it? Acute triangle Right triangle Obtuse triangle

Let's analyze each triangle step by step. --- ### **Triangle (a) with sides 9, 13, and 14** 1. **Compute the sum of the squares of the shorter lengths:** \[ 9^{2} + 13^{2} = 81 + 169 = 250 \] \[ \boxed{250} \] 2. **Compute the square of the longest length:** \[ 14^{2} = 196 \] \[ \boxed{196} \] 3. **Determine the kind of triangle:** - **Compare the sum of the squares of the shorter sides to the square of the longest side:** \[ 250 > 196 \] - **Conclusion:** Since the sum is greater than the square of the longest side, the triangle is **Acute**. **Answer:** - Acute triangle --- ### **Triangle (b) with sides 10, 24, and 26** 1. **Compute the sum of the squares of the shorter lengths:** \[ 10^{2} + 24^{2} = 100 + 576 = 676 \] \[ \boxed{676} \] 2. **Compute the square of the longest length:** \[ 26^{2} = 676 \] \[ \boxed{676} \] 3. **Determine the kind of triangle:** - **Compare the sum of the squares of the shorter sides to the square of the longest side:** \[ 676 = 676 \] - **Conclusion:** Since the sum is equal to the square of the longest side, the triangle is **Right**. **Answer:** - Right triangle ---