Question

The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.

Answer 1

Let hypotenuse=h, and other sides by x and y (x bigger than y). As per the question, 

h = 17 ,  X² + y² = 17 X 17 

⇒  x² + y² = 289 ..... (i) 

In second scenario, sides become Sy and 2x, new h becomes 50 cm 

⇒ (5y)² + (2x)² = 50 x 50 

⇒ 25y² + 4x²= 2500 

⇒ (21y² + 4 y² )+ 4x² = 2500  ..... (ii) 

Putitng (i) in (ii), we get: 

21y² + 4(289) = 2500 

⇒ 21y²= 1344 

⇒ y² = 64 

Hence y = 8cm.

Putting this is (i), we get 

⇒ x²= 289 - 64 = 225 

⇒ x= 25cm 

Hence, the sides are 8, 15, 17 cm.