Question

if each side of an equilateral triangle is increased by 2m, then its area is increased by 3√3 m2. find the length of each side and its area

Answer 1

let each side of equilateral triangle
= a m

since , we know that

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original area of equilateral triangle

= √3 /4 a^2
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given side is increased by 2 m

new side =( a + 2 ) m

new area = √3 / 4 ( a + 2 )^2

according to question :

√3 / 4 ( a + 2 )^2 = √3 a^2 / 4 + 3 √3

√3 ( a^2 + 4 + 4a )=4(√3 a^2 + 12√3 ) 4

√3 a^2 + 4√3 + 4√3 a = √3 a^2 + 12√3

4 √3 a = 8 √3

a = 8 √3/ 4√3

a = 2 m

area of equilateral triangle =√3 /4 (a)^2

= √3 /4 × (2)^2 = √3

therefore
length of each side of the equilateral triangle = 2 m and area = √3 m^2

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Your Answer:side = 2 m, area =√3 m^2
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