Question

The following triplets form the length in cm of the sides of a triangle. State which of them form right- angled triangles. 7,8,9
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Answer 1

We know that,

A right angled triangle has a base, perpendicular height and a hypotenuse.

The hypotenuse is the longest side. The height and base make a 90° angle.

There is a theorem know as Pythagoras theorem.

It states that,

The sum of the square of the height and

the square of the base, is equal to the

square of the hypotenuse.

So, let us take the height as AB, base as BC and hypotenuse as CA.

Therefore, using Pythagoras theorem, we can say thatCA²=AB²+ BC²

Here, in the first option there are three sides.

We know that the length of the hypotenuse is 20 cm, because it is the longest side of a right angled triangle.

So, hypotenuse = CA = 20 cm

CA²=AB²+ BC²

= 16² +12²

= 256 + 144

= 400

CA² = 400 cm

Therefore, CA = √400 = √20 × 20 = 20 cm

This proves that a right angled triangle with sides 12 cm, 16 cm and 20 cm, is possible.

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And we don't need to get concerned about which one is base and which one is height. That's because when we add, in both cases answer should be same.

But still, I will consider

Height = AB = 16 cm

and Base = BC = 12cm

Using Pythagoras theorem,

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