Equilateral Triangle Area Problem! 📐 OTET 2024 Math Sujit Sir

Описание: Equilateral Triangle Area Problem! 📐 OTET 2024 Math Sujit Sir #shorts
Sujit Sir solves the OTET 2024 Paper 2 Math question in this short!

► Question 99: On decreasing the sides of an equilateral triangle by 4 cm, its area decreases by 24√3 cm². What is the length of the sides of the triangle? (A) 14 cm (B) 12 cm (C) 16 cm (D) 10 cm

► Solution: (A) 14 cm

This is a classic mensuration problem from the OTET 2024 exam. Sujit Sir shows you the fastest way to solve it! Don't get stuck in complicated calculations. Learn the direct formula and algebraic trick to find the answer in seconds.

Step-by-Step Solution:
1. Let the original side of the equilateral triangle be 's'. 2. The original area (A1) is = (s²√3) / 4 3. The new side is 's - 4'. 4. The new area (A2) is = ((s - 4)²√3) / 4

5. The problem states the decrease in area (A1 - A2) is 24√3. (s²√3) / 4 - ((s - 4)²√3) / 4 = 24√3

6. We can cancel √3 from all terms: s²/4 - (s - 4)²/4 = 24

7. Multiply all terms by 4 to remove the denominator: s² - (s - 4)² = 96

8. Now, use the "difference of squares" formula (a² - b² = (a+b)(a-b)): a = s b = (s - 4)

[s + (s - 4)] * [s - (s - 4)] = 96 [2s - 4] * [s - s + 4] = 96 [2s - 4] * [4] = 96

9. Divide by 4: 2s - 4 = 24 2s = 28 s = 14 cm

The original side length was 14 cm!

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