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 2 sides of a triangle should be greater than the third side

(ii) The difference of any 2 sides should be less than the third side. For a triangle to be a right angle triangle, there is an additional condition.

Pythagoras theorem: In a right angled triangle, square of the hypotenuse is equal to sum of squares of other 2 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,

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

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

${13}^2=5^2+{12}^2$

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

So, A is the correct option.