Question 31 of 42intermediate🔧 ApplyNumerical3 marks

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

Correct Answer

36 cm

Exercise: END-OF-CHAPTER EXERCISES | Q: 4 | (Page 32)
For More Understanding

Explanation

To find the perimeter, we first need the lengths of all three sides. We use the 'half base times height' formula to find the second leg from the given area. Once both legs are known, the Baudhāyana–Pythagoras theorem is applied to find the hypotenuse. Finally, the perimeter is calculated by summing the three sides.

Solution Steps

  1. Step 1: Find the other leg using the area formula: Area = ½ × base × height. Given Area = 54 sq. cm and one leg = 12 cm, 54 = ½ × 12 × height. So, 54 = 6 × height, which gives height = 9 cm.

  2. Step 2: Find the hypotenuse using the Baudhāyana–Pythagoras theorem: Hypotenuse² = (12)² + (9)² = 144 + 81 = 225. Therefore, Hypotenuse = 15 cm.

  3. Step 3: Calculate the perimeter by adding all three sides: Perimeter = 12 cm + 9 cm + 15 cm = 36 cm.

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