Question

for problems 6 - 9, state whether a triangle with the given side lengths is a right triangle.

1. 5, 12, 13
2. 6, 8, 11
3. 7, 7, 10
4. \frac{9}{2}, 6, \frac{15}{2}

Explanation:

Problem 6: Check Pythagorean theorem

Calculate squares of sides: $5^2=25$, $12^2=144$, $13^2=169$. Sum of smaller squares: $25+144=169=13^2$.

Problem 7: Check Pythagorean theorem

Calculate squares of sides: $6^2=36$, $8^2=64$, $11^2=121$. Sum of smaller squares: $36+64=100≠121$.

Problem 8: Check Pythagorean theorem

Calculate squares of sides: $7^2=49$, $7^2=49$, $10^2=100$. Sum of smaller squares: $49+49=98≠100$.

Problem 9: Check Pythagorean theorem

Calculate squares of sides: $(\frac{9}{2})^2=\frac{81}{4}$, $6^2=36=\frac{144}{4}$, $(\frac{15}{2})^2=\frac{225}{4}$. Sum of smaller squares: $\frac{81}{4}+\frac{144}{4}=\frac{225}{4}=(\frac{15}{2})^2$.

Answer:

1. Yes
2. No
3. No
4. Yes