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Which triplets of numbers cannot possibly represent the sides of a right triangle?
- a)15, 20, 25
- b)8, 9, 10
- c)16, 20, 12
- d)2.5, 6.5, 6
Correct answer is option 'B'. Can you explain this answer?
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Which triplets of numbers cannot possibly represent the sides of a rig...
Explanation:
To determine if a triplet of numbers can represent the sides of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
Where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
To determine if a triplet of numbers can represent the sides of a right triangle, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides.
Checking the triplets:
a) 15, 20, 25
- The longest side is 25.
- Using the Pythagorean theorem: 25^2 = 15^2 + 20^2
- Simplifying: 625 = 225 + 400
- This equation is true, so the triplet can represent the sides of a right triangle.
b) 8, 9, 10
- The longest side is 10.
- Using the Pythagorean theorem: 10^2 = 8^2 + 9^2
- Simplifying: 100 = 64 + 81
- This equation is false, so the triplet cannot represent the sides of a right triangle.
c) 16, 20, 12
- The longest side is 20.
- Using the Pythagorean theorem: 20^2 = 16^2 + 12^2
- Simplifying: 400 = 256 + 144
- This equation is true, so the triplet can represent the sides of a right triangle.
d) 2.5, 6.5, 6
- The longest side is 6.5.
- Using the Pythagorean theorem: 6.5^2 = 2.5^2 + 6^2
- Simplifying: 42.25 = 6.25 + 36
- This equation is true, so the triplet can represent the sides of a right triangle.
Conclusion:
The only triplet of numbers that cannot represent the sides of a right triangle is 8, 9, 10.
To determine if a triplet of numbers can represent the sides of a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
The Pythagorean theorem can be written as:
c^2 = a^2 + b^2
Where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
To determine if a triplet of numbers can represent the sides of a right triangle, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides.
Checking the triplets:
a) 15, 20, 25
- The longest side is 25.
- Using the Pythagorean theorem: 25^2 = 15^2 + 20^2
- Simplifying: 625 = 225 + 400
- This equation is true, so the triplet can represent the sides of a right triangle.
b) 8, 9, 10
- The longest side is 10.
- Using the Pythagorean theorem: 10^2 = 8^2 + 9^2
- Simplifying: 100 = 64 + 81
- This equation is false, so the triplet cannot represent the sides of a right triangle.
c) 16, 20, 12
- The longest side is 20.
- Using the Pythagorean theorem: 20^2 = 16^2 + 12^2
- Simplifying: 400 = 256 + 144
- This equation is true, so the triplet can represent the sides of a right triangle.
d) 2.5, 6.5, 6
- The longest side is 6.5.
- Using the Pythagorean theorem: 6.5^2 = 2.5^2 + 6^2
- Simplifying: 42.25 = 6.25 + 36
- This equation is true, so the triplet can represent the sides of a right triangle.
Conclusion:
The only triplet of numbers that cannot represent the sides of a right triangle is 8, 9, 10.
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Community Answer
Which triplets of numbers cannot possibly represent the sides of a rig...
To determine whether the sides of a right angled triangle are possible we can use the Pythagoras theorem.
Which is- the square of the longest side of the triangle is equal to the square of the height and base of the triangle
15,20,25
The longest side is 25
25^ = 20^ + 15^
625=400+225
Hence, this triangle is possible
8,9,10
The longest side is 10
10^=8^+9^
100 is not equal to 64+81
16,20,12
The longest side is 20
20^=16^+12^
400=256+144
Hence, this triangle is possible
2.5,6.5,6
The longest side is 6.5
6.5^=2.5^+6^
42.25=6.25+36
Hence, the triangle is possible.
Which is- the square of the longest side of the triangle is equal to the square of the height and base of the triangle
15,20,25
The longest side is 25
25^ = 20^ + 15^
625=400+225
Hence, this triangle is possible
8,9,10
The longest side is 10
10^=8^+9^
100 is not equal to 64+81
16,20,12
The longest side is 20
20^=16^+12^
400=256+144
Hence, this triangle is possible
2.5,6.5,6
The longest side is 6.5
6.5^=2.5^+6^
42.25=6.25+36
Hence, the triangle is possible.
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Which triplets of numbers cannot possibly represent the sides of a right triangle?a)15, 20, 25b)8, 9, 10c)16, 20, 12d)2.5, 6.5, 6Correct answer is option 'B'. Can you explain this answer?
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