Question

The smallest side of a right angled triangle is 13 cm , then its hypotenuse will be
a) 84 cm
b) 85 cm
c) 86 cm
d) None of the above

Answer 1

The correct answer is 84 cm

If the shortest side is 13 then you can use the two numbers whos squares differ by 132.

The difference between consecutive squares is consecutive odd numbers.

The difference between (n)^2 and (n+1)^2 is (2n+1)

Since our difference is 13^2=169, this makes n

n=(169–1)/2=84

Answer 2

We know that for any natural number n > 1, then (n, n^2 - 1/2, n^2 + 1/2) are Pythagorean triplets.!

= > n^2 - 1/2

= > 169 - 1/2

= > 168/2

= > 84.

Hence,the largest side of the right angled triangle is 84cm.

Now,

We know that Hypotenuse = (Shorter side)^2 + (Larger side)^2

=> Hypotenuse)^2 = (13)^2 + (84)^2

= > (Hypotenuse)^2 = 169 + 7056

= > (Hypotenuse)^2 = 8225

= > Hypotenuse = 85cm.

Therefore, the hypotenuse = 85cm. - Option (B).

Hope it helps!