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Area of an equilateral triangle = √3/4 a² ( a is its side)
increased side = a + 30a/100 = 13a/10
New area = √3/4 (13a/10)²
=( 169√3 a²) / 400
So increase in area=
= (169√3a² /400) - (√3a² /4 )
= 69√3a² / 400 …………… increase in area
So, percentage increase =
( increase / original area ) * 100
[ {69√3a²/400} / {√3/4 a²} ] * 100
69% increase in area
hope it helps you
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Answer:
Option(D)
Step-by-step explanation:
Let the Initial side of an equilateral triangle be 'x' cm.
Then, Initial area = (√3/4) x² cm.
Given that Side is increased b 30%.
Then, Final area = (√3/4) * 130% of x
= (√3/4) * (130x/100)²
= (√3/4) * (13x/10)²
= (169√3x²)/400
∴ Increase in area = (169√3x²/400 - √3x²/4)
= (69√3x²)/400
∴ Increase% = (69√3x²/400 * 4/√3x² * 100)%
= 69%.
Therefore, Increase in area is 69%.
Hope it helps!