W. Which measurements could NOT represent the side lengths of a right triangle? \( 10 \mathrm{~cm}, 24 \mathrm{~cm}, 26 \mathrm{~cm} \) \( 6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm} \) \( 4 \mathrm{~cm}, 6 \mathrm{~cm}, 10 \mathrm{~cm} \) \( 12 \mathrm{~cm}, 35 \mathrm{~cm}, 37 \mathrm{~cm} \)

We need to verify if the given sets can satisfy the Pythagorean theorem. For a right triangle with side lengths \(a\), \(b\), and hypotenuse \(c\) (where \(c\) is the largest), the equation is: \[ a^2 + b^2 = c^2 \] 1. For \(10 \mathrm{~cm}, 24 \mathrm{~cm}, 26 \mathrm{~cm}\): - Largest side: \(26 \mathrm{~cm}\) - Check: \[ 10^2 + 24^2 = 100 + 576 = 676 \] \[ 26^2 = 676 \] Since \(676 = 676\), this set forms a right triangle. 2. For \(6 \mathrm{~cm}, 8 \mathrm{~cm}, 10 \mathrm{~cm}\): - Largest side: \(10 \mathrm{~cm}\) - Check: \[ 6^2 + 8^2 = 36 + 64 = 100 \] \[ 10^2 = 100 \] Since \(100 = 100\), this set forms a right triangle. 3. For \(4 \mathrm{~cm}, 6 \mathrm{~cm}, 10 \mathrm{~cm}\): - Largest side: \(10 \mathrm{~cm}\) - Check: \[ 4^2 + 6^2 = 16 + 36 = 52 \] \[ 10^2 = 100 \] Since \(52 \neq 100\), this set does not form a right triangle. 4. For \(12 \mathrm{~cm}, 35 \mathrm{~cm}, 37 \mathrm{~cm}\): - Largest side: \(37 \mathrm{~cm}\) - Check: \[ 12^2 + 35^2 = 144 + 1225 = 1369 \] \[ 37^2 = 1369 \] Since \(1369 = 1369\), this set forms a right triangle. Thus, the measurements that could NOT represent the side lengths of a right triangle are: \[ 4 \mathrm{~cm},\, 6 \mathrm{~cm},\, 10 \mathrm{~cm} \]