Question

if the sides of a triangle are a = 10, b = 24, and c = 26, verify if the triangle is a right triangle. a. cannot be determined b. yes, because a² + b² = c² c. no, because a² + b² < c² d. no, because a² + b² > c² what is the pythagorean theorem? a. a² + b² = c² b. a² - b² = c² c. a + b = c d. a × b = c

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle, the relationship between the sides is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side).

Step2: Calculate $a^{2}+b^{2}$

Given $a = 10$, $b = 24$, then $a^{2}=10^{2}=100$, $b^{2}=24^{2}=576$, so $a^{2}+b^{2}=100 + 576=676$.

Step3: Calculate $c^{2}$

Given $c = 26$, then $c^{2}=26^{2}=676$.

Step4: Compare

Since $a^{2}+b^{2}=676$ and $c^{2}=676$, we have $a^{2}+b^{2}=c^{2}$, so the triangle is a right - triangle.
For the second question, the Pythagorean Theorem is $a^{2}+b^{2}=c^{2}$.

Answer:

1. b. Yes, because $a^{2}+b^{2}=c^{2}$
2. a. $a^{2}+b^{2}=c^{2}$