Question

which of the following could be the measures of the sides of a right triangle? a) \\(sqrt{3}, sqrt{4}, sqrt{5}\\) b) \\(sqrt{5}, sqrt{12}, sqrt{13}\\) c) \\(8, 15, 17\\) d) \\(9, 16, 25\\)

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the longest side.

Step2: Test Option A

Calculate squares: $(\sqrt{3})^2=3$, $(\sqrt{4})^2=4$, $(\sqrt{5})^2=5$. Check: $3+4
eq5$.

Step3: Test Option B

Calculate squares: $(\sqrt{5})^2=5$, $(\sqrt{12})^2=12$, $(\sqrt{13})^2=13$. Check: $5+12
eq13$.

Step4: Test Option C

Calculate squares: $8^2=64$, $15^2=225$, $17^2=289$. Check: $64+225=289$.

Step5: Test Option D

Calculate squares: $9^2=81$, $16^2=256$, $25^2=625$. Check: $81+256
eq625$.

Answer:

C) 8, 15, 17