Question

Among the following options, the sides of a right-angled triangle that have the hypotenuse of rational value is .

• A. 5 and 13
• B. 3 and 5
• C. 6 and 8
• D. 24 and 25

Answer 1

The correct option is C 6 and 8

In a right triangle, square of a hypotenuse is sum of squares of perpendicular sides.

If the perpendicular sides are 24 and 25,
Hypotenuse $=\sqrt{{24}^2+{25}^2}=\sqrt{1,201}$, which is irrational.

If the perpendicular sides are 5 and 13,
Hypotenuse $=\sqrt{5^2+{13}^2}=\sqrt{194}$, which is irrational.

If the perpendicular sides are 3 and 5,
Hypotenuse $=\sqrt{3^2+5^2}=\sqrt{34}$, which is irrational.

If the perpendicular sides are 6 and 8,
Hypotenuse $=\sqrt{6^2+8^2}=\sqrt{100}$ = 10, which is rational.

So, 6 and 8 are the perpendicular sides for which the hypotenuse is rational.