Question

Which of the following could be the side lengths of a right triangle?

a. 3, 13 and 14
b. 4, 5, and 6
c. 4, 9, and 10
d. 5, 10, and 15
e. 5, 12, and 13

Answer 1

OptionE)5,12,13

Explanation:

If a triangle is a right triangle, then the lengths of its sides satisfy the Pythagorean Theorem,
`a^(2)+b ^(2) =c^(2)` To determine which choice is correct, test each set of values by substituting them into the Pythagorean Theorem. Start with the first set of numbers: 3, 13, and 14.

`3^(2) + 13^(2) = 14^(2) \\9+169=196`

`178=196`

Since the result is not a true equality, the first set of values does not represent the side lengths of a right triangle. Test the other four choices. The only values that satisfy the Pythagorean Theorem are 5, 12, and 13.

`5^(2) +12^(2) = 13^(2) \\25+144=169\\169=169`

Hence 5,12,and 13 are side lengths of a right triangle

Answer 2

e) 5, 12, and 13

Explanation:

To find if the given triangle is right triangle, use Pythagorean theorem.

If the sum of the squares of the two smaller sides equals the square of the largest side, then the triangle is a right angle triangle.

Sum of the two smallest side = 5² + 12²

= 25 + 144

= 169

Square of the largest side = 13²

= 169

sum of squares of smallest side =square of the largest side.

So, 5 , 12 , 13 form a right triangle.