Question

The ratio of the two legs of a right-angled triangle is $3:1$. If the lengths of the legs are whole numbers, what can be the possible value of the hypotenuse?

• A. $\sqrt{40}$
• B. $\sqrt{47}$
• C. $\sqrt{55}$
• D. $\sqrt{63}$

Answer 1

The correct option is A $\sqrt{40}$

The legs of a right angled triangle are in the ratio $3:1$ and they are whole numbers.

The possibilities are as listed below:

$3,1$ - The hypotenuse becomes $\sqrt{(3{)}^2+(1{)}^2}=\sqrt{10}$

$6,2$ - The hypotenuse becomes $\sqrt{(6{)}^2+(2{)}^2}=\sqrt{40}$

$9,3$ - The hypotenuse becomes $\sqrt{(9{)}^2+(3{)}^2}=\sqrt{90}$

Thus, the hypotenuse will always be square root of a multiple of $10$, which is in option A.