Question

25. The length of each side of an equilateral triangle is trippled, the percent of area will be increased
(a) 300%
(b) 800%
(c) 200%
(d) 100%
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Answer 1

Answer:

Let the length of each side of equilateral triangle initially be 'x'.

Then, the new sides = 3x

Initial Area = Root3/4 a^2

Root 3/4 x^2

New Area = Root3/4 a^2

Root 3/4 (3x)^2

= Root 3/4 9x^2

Therefore , Percentage in increase

=Root 3/4 9x^2 - Root 3/4 x^2

=900% -100%

=800%

Answer 2

Answer:

(b) 800 %

Step-by-step explanation:

Area of an equilateral triangle = $\frac{\sqrt{3} }{4}(side)^2$

Let each side of the equilateral triangle = a

then original area =  $\frac{\sqrt{3} }{4}a^2$

Now, new side = 3a

Then, new area =   $\frac{\sqrt{3} }{4}(3a)^2 = \frac{\sqrt{3} }{4}9a^2$

Therefore, Increase in area =  $\frac{\sqrt{3} }{4}(9a^2- a^2) = \frac{\sqrt{3} }{4} 8a^2 = 2\sqrt{3} a^2$

Percentage increase= $\frac{2\sqrt{3a^2} }{\frac{\sqrt{3} a^2 }{4} } * 100$ = 800 %

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