Question

The hypotenuse of a right triangle is 3 root5​cm. If the smaller side is tripled and the larger side is doubled, the new hypotenuse will be 15cm. Find the length of each side.

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Answer 1

Given :-

• Original hypotenuse = 3√5 cm.
• New hypotenuse = 15 cm.

To Find :-

• Length of each side of the right triangle.

Solution :-

Let:-

• Smaller side of the right triangle = x cm
• Larger side of the right triangle = y cm

A.T.Q,

⇒ x² + y² = (3√5)² [Using Pythagoras Theorem]

⇒ x² + y² = 45............( 1 )

Also, if the smaller side is tripled and the larger side is doubled, the new hypotenuse is 15 cm,

⇒ (3x)² + (2y)² = 15²

⇒ 9x² + 4y² = 225.....( 2 )

From equation ( 1 ), we get,

⇒ y² = 45 - x²

Putting y² = 45 - x² in ( 2 ), we get,

⇒ 9x² + 4(45 - x²) = 225

⇒ 9x² - 4x² + 180 = 225

⇒ 5x² + 180 = 225

⇒ 5x² = 45

⇒ x² = 9

⇒ x = √9 = ±3

But, length of side cannot be negative, therefore,

⇒ x = 3

Putting x = 3 in ( 1 ), we get,

⇒ 9 + y² = 45

⇒ y² = 36

⇒ y = 6

Hence,

• Length of the smaller side = 3 cm.
• Length of the larger side = 6 cm.