The hypotenuse of a right triangle is cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be cm. How long are the legs of the triangle?

Question

Philoid · Accepted Answer

Let the smaller leg be ‘a’ and longer leg be ‘b’.

Hypotenuse² = length² + breadth²

Given, hypotenuse of a right triangle is cm

⇒ 9 × 10 = a² + b²

⇒ a² + b² = 90 -------- (1)

Now, the smaller leg is tripled and the longer leg doubled, new hypotenuse is cm.

⇒ (3a)² + (2b)² = 81 × 5

⇒ 9a² + 4b² = 405 -------- (2)

Multiplying (1) by 4 and subtracting from eq 2

⇒ 5a² = 45

⇒ a² = 9

⇒ a = 3

Thus, 9 + b² = 90

⇒ b² = 81

⇒ b = 9