Question

The Hypotenuse of a right Triangle is 3√10 cm. If the Smaller by is tripled and longer leg doubled , now hypotenuse will be 9√5 cm. How long are the legs of the Triangle.

Answer 1

Let the smaller perpendicular side be x cm and the larger perpendicular side be y cm.

Given : Length of the hypotenuse = 3√10 cm

⇒ x² + y² = (3√10)² = 90 ....(1)

Now, when the smaller side is tripled the smaller side becomes 3x cm.

and when the larger side is doubled the larger side becomes 2y cm.

also the hypotenuse becomes 9√5 cm.

⇒ (3x)² + (2y)² = (9√5)²

⇒ 9x² + 4y² = 405

⇒ 5x² + 4x² + 4y² = 405

⇒ 5x² + 4(x² + y²)= 405

⇒ 5x² + 4 × 90 = 405 (from (1))

⇒ 5x² + 360 = 405

⇒ 5x² = 405 - 360 = 45

⇒ x² = 45/5 = 9

⇒ x = 3

Putting the value of x in (1) we get

3² + y² = 90

⇒ 9 + y² = 90

⇒ y² = 90 - 9 = 81

⇒ y = 9

Hence, the required sides of the triangle are 3 cm and 9 cm.