The three side lengths of four triangles are given. Which triangle is a right triangle?
Triangle 1: √13, 6, 7
Triangle 2: 7, 8, 13
Triangle 3: 10, 11, 12
Triangle 4: √10, 9, 8
The three side lengths of four triangles are given. Which triangle is a right triangle? Triangle 1: √13, 6, 7 Triangle 2: 7, 8, 13 Triangle 3: 10, 11, 12 Triangle 4: √10, 9, 8
Share
To determine if a 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 other two sides.
Let’s examine each triangle:
1. Triangle 1: Sides are √13, 6, 7
– Hypotenuse: 7
– Check: (7^2 = 49) and (√13^2 + 6^2 = 13 + 36 = 49).
– This is a right triangle.
2. Triangle 2: Sides are 7, 8, 13
– Hypotenuse: 13
– Check: (13^2 = 169) and (7^2 + 8^2 = 49 + 64 = 113).
– Not a right triangle.
3. Triangle 3: Sides are 10, 11, 12
– Hypotenuse: 12
– Check: (12^2 = 144) and (10^2 + 11^2 = 100 + 121 = 221).
– Not a right triangle.
4. Triangle 4: Sides are √10, 9, 8
– Hypotenuse