The side lengths of different triangles are given. Which triangle is a right triangle?
6, 7, 13
√21, √99, 11
10, 12, 15
√35, √14, 7
The side lengths of different triangles are given. Which triangle is a right triangle? 6, 7, 13 √21, √99, 11 10, 12, 15 √35, √14, 7
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To determine which triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let’s check each set of side lengths:
1. 6, 7, 13:
( 13^2 = 169 )
( 6^2 + 7^2 = 36 + 49 = 85 )
Not a right triangle.
2. √21, √99, 11:
( 11^2 = 121 )
( (√21)^2 + (√99)^2 = 21 + 99 = 120 )
Not a right triangle.
3. 10, 12, 15:
( 15^2 = 225 )
( 10^2 + 12^2 = 100 + 144 = 244 )
Not a right triangle.
4. √35, √14, 7:
( 7^2 = 49 )
( (√35)^2 + (√14)^2 = 35 + 14 = 49 )
This is a right triangle.
The triangle with the side lengths **√35