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), (B)

The correct options are
A

10 cm , 6 cm , 8 cm

B

2 cm , 17 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 angle triangle, there is an additional condition.

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

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

Considering each of the given options,

${10}^2=6^2+8^2$
${17}^2=8^2+{15}^2$
$9^2\ne 5^2+4^2$
${27}^2\ne {13}^2+{15}^2$