Three sides of right angled triangle are three consecutive even numbers. Find the hypotenuse
Answers
(6,8,10) = 36 + 64 =100
An interesting fact: a Pythagorean Triplealways consists of: all even numbers, or. two odd numbers and an even number.
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hypotenuse = 10 if Three sides of right angled triangle are three consecutive even numbers.
Step-by-step explanation:
Three sides of right angled triangle are three consecutive even numbers
Let say hypotenuse = 2n
then other two sides will be 2n - 2 & 2n - 4
(2n)² = (2n - 2)² + (2n - 4)²
=> 4n² = 4n² + 4 - 8n + 4n² + 16 - 16n
=> 0 = 4n² - 24n + 20
=> 0 = n² - 6n + 5
=> n² - n - 5n + 5 = 0
=> n(n-1) -5(n - 1) = 0
=> (n - 5) (n - 1) = 0
=> n = 5 or 1
n = 1 not possible as then other sides will be 0 & - 2 ( which is not possible)
hence n = 5
hypotenuse = 2n = 2 * 5 = 10
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