The hypotenuse of a right triangle is \(3\sqrt{10}\) cm. If the small

1.	The hypotenuse of a right triangle is \(3\sqrt{10}\) cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be \(9\sqrt{5}\) cm. How long are the legs of the triangle
Answer» Let the smaller leg be ‘a’ and longer leg be ‘b’. Hypotenuse² = length² + breadth² Given, hypotenuse of a right triangle is \(3\sqrt{10}\) cm ⇒ 9 × 10 = a² + b² ⇒ a²+ b² = 90 -------- (1) Now, the smaller leg is tripled and the longer leg doubled, new hypotenuse is \(9\sqrt{5}\) 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

The hypotenuse of a right triangle is \(3\sqrt{10}\) cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be \(9\sqrt{5}\) cm. How long are the legs of the triangle

Answer»

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

Hypotenuse² = length² + breadth²

Given, hypotenuse of a right triangle is \(3\sqrt{10}\) cm

⇒ 9 × 10 = a² + b²

⇒ a²+ b² = 90 -------- (1)

Now, the smaller leg is tripled and the longer leg doubled, new hypotenuse is \(9\sqrt{5}\) 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