Question

(2) A right-angled triangle has sides 12 and 5cm. what is the
length of hypotenuse of this triangle?​

Answer 1

The Pythagorean theorem will give the answer for any pair of values of the two sides. If the two input values are integers, in most cases the result will not be an integer because you’re taking the square root of an integer.

However, there are special cases, known as Pythagorean triples, where all three values (2 inputs and 1 result) will be integers. You just happened to pick one of them: 5, 12, 13. Another triple is 3, 4, 5.

I’m betting that anyone who answered this question or contemplated answering it would have recognized that 5, 12 are part of a Pythagorean triple and would have known the answer (13) without having to do the calculation.

For extra credit, do some research on triples and see what patterns they form. You’ll find it interesting.

regards,

prakash,

Answer 2

Answer:

We can get this answer by using Pythagoras Theorem.

Given :-

• Sides ( assume AB and BC ) = 12 cm and 5 cm

Formula :-

• AB^2 + BC^2 = AC^2

Solution :-

• Length of the third side ( AC ) :-
• 12^2 + 5^2 = AC^2
• or, 144 + 25 = AC^2
• or, 169 = AC^2
• or, √169 = AC
• or, 13 = AC

Hence,the length of the third side is 13 cm.