If one of the sides of a right triangle has length of 10, which of the

Solution:

We are asked which of the following pair can be sides of right angle triangle along with a side that has a length of 10

We know that the sides of a right-angle triangle follow the Pythagoras theorem which states \(hypotenuse^2=base^2+perpendicular^2\)


I. 6 and 8

If 6, 8 and 10 are sides of a right-angle triangle, then 10 has to be the hypotenuse because it is the largest

and \(10^2=6^2+8^2\) has to satisfy which it does
\(⇒100=100\)


II. 15/2 and 25/2

If \(\frac{15}{2}\), \(\frac{25}{2}\) and 10 are sides of a right-angle triangle, then \(\frac{25}{2}\) has to be the hypotenuse because it is the largest

and \((\frac{25}{2})^2=(\frac{15}{2})^2+10^2\) has to satisfy which it does
\(⇒\frac{625}{4}=\frac{625}{4}\)


III. 40/3 and 50/3

If \(\frac{40}{3}\), \(\frac{50}{3}\) and 10 are sides of a right-angle triangle, then \(\frac{50}{3}\) has to be the hypotenuse because it is the largest

and \((\frac{50}{3})^2=(\frac{40}{3})^2+10^2\) has to satisfy which it does
\(⇒\frac{2500}{9}=\frac{2500}{9}\)


Thus, we see that all the three pairs can be the sides of right angle triangle


Hence the right answer is Option E