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Answers
In the given sides, 1. a = 6 cm, b = 8 cm, and c = 10 cm are sides of the right-angle triangle.
Given:
Sides of the length of triangles are given below
1. a = 6 cm, b = 8 cm, and c = 10 cm
2. a = 5 cm, b = 8 cm, and c = 11 cm
To find:
Which of the given sides are sides of the right-angle triangle?
Solution:
Right angle triangle:
The triangle in which one of the angles is equal to 90° is known as a Right angle triangle. In a right-angle triangle, the sum of the squares of the two sides will equal the square of the hypotenuse.
And the relation can be written as
Hypotenuse² = side² + side²
Now check which of the given sides will follow the above condition,
1. a = 6 cm, b = 8 cm, and c = 10 cm
Here 10 cm is the longest side, so take c as the length of the hypotenuse
If these sides of a right-angle triangle then
10² must be equal to the sum 8² and 6²
=> 10² = 8² + 6²
=> 100 = 64 + 36
=> 100 = 100 [ which is true]
Therefore,
1. a = 6 cm, b = 8 cm, and c = 10 cm are sides of the right-angle triangle.
2. a = 5 cm, b = 8 cm, and c = 11 cm
Here 11 cm is the longest side, so take c as the length of the hypotenuse
If these sides of a right-angle triangle then
11² must be equal to the sum 8² and 5²
=> 11² = 8² + 5²
=> 121 = 64 + 25
=> 121 = 89 [ which is not true]
Therefore,
2. a = 5 cm, b = 8 cm, and c = 11 cm are not the sides of the right-angle triangle.
Therefore,
In the given sides, 1. a = 6 cm, b = 8 cm, and c = 10 cm are sides of the right-angle triangle.
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