Mensuration Practice Test 6

Question : 35 of 40

Marks: +1, -0

If the length of each side of an equilateral triangle is increased by 2 unit. The area is found to be increased by 3 +

√3

square units. The length of each side of the triangle is:

Solution:

Area of the equilateral triangle =

√3/4 a^2

A =

√3/a a^2

... (i)
New area of equilateral triangle
= A +

(3+√3)

√3/4(a+2)^2

... (ii)
Subtracting (i) from (ii),

A+(3+√3)

- A =

√3/4 ((a+2)^2-a^2)

3+√3

√3/4 (a^2+ 4 + 4a -a^2)

3+√3

√3+√3a

3 =

√3a

a =

√3

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