The area of a right-angled triangle is 54 sq. cm. One of its legs has length 12 cm. Find its perimeter.

Step-by-step solution

Idea: In a right-angled triangle the two legs are a base and a height, so the area gives the other leg; then use the Baudhāyana–Pythagoras theorem.

1. 12 × 12 × x = 54 ⇒ 6x = 54 ⇒ x = 9 cm (other leg).1 mark
2. Hypotenuse = √(12² + 9²) = √(144 + 81) = √225 = 15 cm.1 mark
3. Perimeter = 12 + 9 + 15 = 36 cm.1 mark

Answer to write in the exam

Common mistakes that cost marks

• Taking 12 cm as the hypotenuse. It is a leg (the question says so).
• Stopping at 9 cm and not adding the hypotenuse.

How this can come in the exam

Try one yourself

A right-angled triangle has area 84 cm² and one leg 24 cm. Find its perimeter.

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