Question

explain if a triangle with the given side lengths is a right triangle.

1. 18, 24, 30
2. 7, 24, 25
3. 10, 24, 25
4. 13, 14, 15

Explanation:

1. Check 18,24,30

Longest side=30. $18^2 + 24^2 = 324 + 576 = 900$, $30^2=900$. Equal, right triangle.

2. Check 7,24,25

Longest side=25. $7^2 + 24^2 = 49 + 576 = 625$, $25^2=625$. Equal, right triangle.

3. Check 10,24,25

Longest side=25. $10^2 + 24^2 = 100 + 576 = 676$, $25^2=625$. Not equal, not right triangle.

4. Check 13,14,15

Longest side=15. $13^2 + 14^2 = 169 + 196 = 365$, $15^2=225$. Not equal, not right triangle.

Answer:

1. 18,24,30: Right triangle (since $18^2 + 24^2 = 30^2$)
2. 7,24,25: Right triangle (since $7^2 + 24^2 = 25^2$)
3. 10,24,25: Not a right triangle (since $10^2 + 24^2

eq 25^2$)

1. 13,14,15: Not a right triangle (since $13^2 + 14^2

eq 15^2$)