Question 30 of 42intermediate🔧 ApplyNumerical3 marks

An isosceles triangle has base 10 cm, and its area is 60 cm². What are the lengths of the equal sides?

Correct Answer

13 cm

Exercise: END-OF-CHAPTER EXERCISES | Q: 3 | (Page 32)
For More Understanding

Explanation

The problem is solved by first finding the height of the isosceles triangle using the 'half base times height' formula with the given area and base. Once the height is known, the Baudhāyana–Pythagoras theorem (as applied to isosceles triangles in the context, where a² - h² = b²) is used to calculate the length of the equal sides.

Solution Steps

  1. Step 1: Let the equal sides be a cm and the base be 2b cm. Given base = 10 cm, so 2b = 10, which gives b = 5 cm.

  2. Step 2: Using the 'half base times height' formula, Area = 1/2 × base × height. Given Area = 60 cm², 60 = 1/2×102 \times 10 × h, which gives h = 12 cm.

  3. Step 3: By the Baudhāyana–Pythagoras theorem for isosceles triangles, a² - h² = b². Substituting the values, a² - 12² = 5², so a² - 144 = 25.

  4. Step 4: Solving for a, a² = 169, which gives a = 13 cm.

PreviousNext