# If Each Side of a Triangle is Doubled, the Find Percentage Increase in Its Area. - Mathematics

If each side of a triangle is doubled, the find percentage increase in its area.

#### Solution

The area of a triangle having sides aband s as semi-perimeter is given by,

A = sqrt(s(s-a)(s-b)(s-c))

Where,

s = (a+b+c)/2

2s = a+b+c

We take the sides of a new triangle as 2a, 2b, 2c that is twice the sides of previous one

Now, the area of a triangle having sides 2a, 2b, and 2and s1 as semi-perimeter is given by,

A_1= sqrt(s_1(s_1-2a)(s_1-2b)(s_1-2c))

Where,

s_1 = (2a+2b+2c)/2

s_1 = (2(a+b+c))/2

s1  =  a+ b+ c

s1 =  2s

Now,

A_1 = sqrt(2s (2s-2a)(2s-2b)(2s-2c))

A_1 = sqrt(2s xx 2 (s-a) xx 2 (s-b) xx 2 (s-c))

A_1 = 4 sqrt(s(s-a)(s-b)(s-c))

A_1 = 4A

Therefore, increase in the area of the triangle

=A1 -A

=4A-A

=3A

Percentage increase in area

=(3A)/A xx 100

= 300%

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.3 | Q 9 | Page 24

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