5 The following triplets form the length in cm of the sides of a triangle. State which of them form right-
angled triangles.
12.16.20
b 7,8,9
e 15, 28, 14
d 5.12, 13
e 16,63,65
f 9, 10, 12.
With Full explanation.
Answers
Answer:
12 cm, 16 cm, 20 cm
Step-by-step explanation:
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 that
CA² = 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
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,
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.
(We can find out why the other options are not correct by simply using the same Pythagoras theorem.)