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If the side of an equilateral triangl...

If the side of an equilateral triangle is decreased by 20%, its area is decreased by (a) 36% (b) 40% (c) 60% (d) 64%

A

`8%`

B

`16%`

C

`36%`

D

`20%`

Text Solution

Verified by Experts

The correct Answer is:
3
Let the side of equilateral triangle =a =10 cm
`because` Area of equilateral triangle `=(sqrt(3))/(4)a^(2)` `therefore` Area of equilateral triangle `=(sqrt(3))/(4)xx(10)^(2)=25sqrt(3)cm^(2)`
Now , new side of equilateral triangle `=(80)/(100)xx10=8cm`
`therefore` New area of equilateral triangle `=(sqrt(3))/(4)xx(8)^(2)=16sqrt(3)cm^(2)`
Required percentage decrease `=((25sqrt(3)-16sqrt(3))/(25sqrt(3)))xx100`
`=(9sqrt(3))/(25sqrt(3))xx100=36%`
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