Question

Q.12 Two right angled triangles have integer side lengths. While all of the
sides have different lengths, the hypotenuses are equal. What is the smallest
length of the hypotenuse?​

Answer 1

Answer:

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Answer 2

5 is the smallest  length of such hypotenuse.

Step-by-step explanation:

Here we need the smallest length of the hypotenuse of a  right angled triangle whose all the sides are non-integers.

For such a case we have Pythagoras theorem:

$h^2=p^2+b^2$

where h, p and b denote thelength of hypotenuse perpendicular and base respectively.

Then we check for the smallest square number that can be represented as the sum of square of two integers we get the number as 25 which can be represented as the sum of square of 3 and square of 4.

Mathematically:

$3^2+4^2=25=5^2$

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TOPIC: Pythagoras theorem, right angled triangle.

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