Question

The lengths of the sides of a right-angled triangle are all given in natural numbers. If two of these numbers are odd and they differ by $50$, then the least possible value for the third side is:

• A. $61$
• B. $60$
• C. $51$
• D. $50$

Answer 1

Answer: (B)

$60$

We can observe,considering general numbers for right angled triangle,
$5^2=3^2+4^2$ (5, 3 are odd and 4 lies between 5, 3)
and ${13}^2=5^2+{12}^2$ (5, 13 are odd and 12 lies between 5, 13)
By trial and error
${61}^2={60}^2+{11}^2$
Since (61, 11 are odd and 61 hypotenuse)
$61-11=50$
Hence, option 'B' is correct.