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When each side of an equilateral triangle is increased by 4 cm, its area increases by 5√3 cm2, then the length of the side of the original triangle is
- A0.5 cm
- B√2 cm
- C2 cm
- D(√2 + 1) cm
Answer not set
Discussion 1
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CCommunity
Let ‘a’ be the side of the equilateral triangle.
Area of the equilateral triangle = A = √3/4 × a2
As per the question,
when a’ = a + 4, A’ = A + 5√3
⇒ √3/4 × a2 + 5√3 = √3/4 × (a + 4)2
⇒ √3/4 × a2 + 5√3 = √3/4 × (a2 + 8a + 16)
⇒ √3/4 × a2 + 5√3 = (√3/4 × a2) + 2√3a + 4√3
⇒ 5√3 = 2√3a + 4√3
⇒ √3 = 2√3 a
⇒ 1 = 2a
⇒ a = ½ = 0.5 cm
Thus, the length of the side of the original triangle is 0.5 cm
Area of the equilateral triangle = A = √3/4 × a2
As per the question,
when a’ = a + 4, A’ = A + 5√3
⇒ √3/4 × a2 + 5√3 = √3/4 × (a + 4)2
⇒ √3/4 × a2 + 5√3 = √3/4 × (a2 + 8a + 16)
⇒ √3/4 × a2 + 5√3 = (√3/4 × a2) + 2√3a + 4√3
⇒ 5√3 = 2√3a + 4√3
⇒ √3 = 2√3 a
⇒ 1 = 2a
⇒ a = ½ = 0.5 cm
Thus, the length of the side of the original triangle is 0.5 cm