Question

If the sides of an equilateral triangle are increased by 20%, 30% and 50% respectively to form anew triangle, what is the percentage increase in the perimeter of the equilateral triangle?​

Answer 1

Step-by-step explanation:

Let the side of an equilateral triangle be --- x

Then perimeter of equilateral triangle ==> 3x

The A/q

==> New sides of triangle is

20%x + x = x + 20/100x => 6x/5

==>

x + 30/100x => 13x/10

==>

x + 50/100x => 3x/2

Now we have a new sides of triangle is

Now, The perimeter of new triangle =>

==> 6x/5 + 13x/10 + 3x/2

==>

$\frac{(12x + 13x + 15x)}{10 } = \frac{40x}{10} = 4x$

Increase in perimeter ==> final perimeter - initial perimeter

Increase in perimeter ==> 4x - 3x

==> x

% increase in perimeter of triangle => (increase / inital perimeter) × 100

%. ==>

$\frac{x}{3x} \times 100 = \: \frac{100}{3} \% = 33.33\%$

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Answer 2

Answer:

$\huge\underline\bold {Answer:}$

Let the sides of the equilateral triangle be x cm. Then, after increase the three sides are

x + 20/100x, x + 30/100x and x + 50/100x,

i.e., x + 0.2x, x + 0.3x and x + 0.5x,

i.e., 1.2x, 1.3x and 1.5x.

Therefore Original perimeter = 3x,

Increased perimeter = 1.2x + 1.3x + 1.5x = 4x

Percent increase in perimeter =(Increase in perimeter ÷ Original perimeter) × 100

$= \frac{(4x - 3x)}{(3x)} \times 100\%$

= 100/3%

Hence percent increase in the perimeter of the equilateral triangle

= 100/3%