Question

q1 - accelerated mathematics gr 8 | lesson: interpreting pythagorean theorem and its co... what type of triangle has sides a = 8, b = 15, and c = 17? a. scalene triangle b. right triangle c. isosceles triangle d. acute triangle if the sides of a triangle are a = 10, b = 24, and c = 26, verify if the triangle is a right triangle. a. no, because a² + b² > c² b. yes, because a² + b² = c² c. no, because a² + b² < c²

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check first triangle with $a = 8$, $b = 15$, $c = 17$

Calculate $a^{2}+b^{2}$: $8^{2}+15^{2}=64 + 225=289$, and $c^{2}=17^{2}=289$. Since $a^{2}+b^{2}=c^{2}$, it is a right - triangle.

Step3: Check second triangle with $a = 10$, $b = 24$, $c = 26$

Calculate $a^{2}+b^{2}$: $10^{2}+24^{2}=100+576 = 676$, and $c^{2}=26^{2}=676$. Since $a^{2}+b^{2}=c^{2}$, it is a right - triangle.

Answer:

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