The perimeter of a right-angled triangle is 60cm and its hypotenuse is 26cm. Find the other two sides.

Given perimeter of right-angled triangle is 60 cm.

hypotenuse = h = 26 cm

Let the other two sides be a & b.

So, a + b + h = 60

⇒ a + b = 60 – 26

⇒ a + b = 34 ...... (i)

By Pythagoras theorem,

⇒ a² + b² = h²

(As shown below:

⇒ a² + b² = 26²

⇒ (a + b)² – 2ab = 676

⇒ 34² – 2ab = 676

⇒ 2ab = 1156 – 676

⇒ 2ab = 480

⇒ ab = 240

Using (a – b)² = a² + b² – 2ab

⇒ (a – b)² = 676 – 2x240

⇒ (a – b)² = 676 – 480

⇒ (a – b)² = 196

⇒ a – b = 14 ...... (ii)

adding (i) &(ii);

⇒ 2a = 48

⇒ a = 24

⇒ b = 10

So, the other two sides are 24 cm & 10cm.