Question 29 of 42intermediate🔧 ApplyNumerical3 marks

An isosceles triangle has perimeter 40 cm; the equal sides are 15 cm each. Find the area of the triangle.

Correct Answer

502\sqrt{2} cm²

Exercise: END-OF-CHAPTER EXERCISES | Q: 2 | (Page 32)
For More Understanding

Explanation

To find the area of the isosceles triangle, we first determine the length of the base using the given perimeter. Then, we calculate the semi-perimeter and apply Heron's formula, which is demonstrated in the context for isosceles triangles. The context also provides a derived formula for isosceles triangles (Area = ba2−b2\sqrt{a² - b²}), which yields the same result.

Solution Steps

  1. Step 1: Find the base of the isosceles triangle. Base = Perimeter - (Sum of equal sides) = 40 - (15 + 15) = 10 cm.

  2. Step 2: Calculate the semi-perimeter (s). s = ½ × (15 + 15 + 10) = ½ × 40 = 20 cm.

  3. Step 3: Apply Heron's formula. Area = √[s(s - a)(s - b)(s - c)] = √[20(20 - 15)(20 - 15)(20 - 10)].

  4. Step 4: Simplify the expression. Area = √[20×520 \times 5 × 5×105 \times 10] = √[5000] = 502\sqrt{2} cm².

PreviousNext