Question

Which of the following numbers can form sides of a right angled triangle?

• A. 10 cm , 6 cm , 8 cm
• B. 2 cm , 17 cm , 9 cm
• C. 4 cm , 5 cm , 9 cm
• D. 13 cm , 27 cm , 15 cm

Answer 1

Answer: (A), (C)

The correct options are
A

10 cm , 6 cm , 8 cm

C

4 cm , 5 cm , 9 cm

The basic condition for any type of triangle is :
(i) The sum of two sides of a triangle should be greater than the third side

(ii) The difference of any two sides should be less than the third side.

For a triangle to be a right angled triangle, there is an additional condition:

Pythagoras theorem: In a right angled triangle, ${\text{Hypotenuse}}^2=$ Sum of squares of other two sides.

That is, $c^2=a^2+b^2$. Also note that the hypotenuse is the largest side in a right triangle.

Considering each of the given options:

A) ${10}^2=6^2+8^2$

B) ${17}^2\ne 2^2+9^2$

C) $5^2=3^2+4^2$

D) ${27}^2\ne {13}^2+{15}^2$

So, A and C are the correct options.