Question

Three sides of right angled triangle are three consecutive even numbers. Find the hypotenuse

Answer 1

(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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Answer 2

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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