Question

which of the measurements form a right triangle? a 5cm, 7cm, 10cm b 17cm, 23cm, 40cm c 10cm, 24cm, 26cm d 9cm, 12cm, 18cm

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.

Step2: Check option A

\(5^{2}+7^{2}=25 + 49=74\), \(10^{2}=100\). Since \(74
eq100\), not a right - triangle.

Step3: Check option B

\(17^{2}+23^{2}=289+529 = 818\), \(40^{2}=1600\). Since \(818
eq1600\), not a right - triangle.

Step4: Check option C

\(10^{2}+24^{2}=100 + 576=676\), \(26^{2}=676\). Since \(10^{2}+24^{2}=26^{2}\), it is a right - triangle.

Step5: Check option D

\(9^{2}+12^{2}=81+144 = 225\), \(18^{2}=324\). Since \(225
eq324\), not a right - triangle.

Answer:

C. 10cm, 24cm, 26cm