Question

if sach side of a triangle is doubled, then find the percentage increase in the area of triangle

​

Answer 1

Answer:

Semi-perimeter of the triangle, s=

2

a+b+c

Area of triangle =

s(s−a)(s−b)(s−c)

.

When each side is doubled, the new sides are 2a,2b,2c.

Hence, new s

′

=

2

2a+2b+2c

=2(

2

a+b+c

)=2s

New area A

′

=

2s(2s−2a)(2s−2b)(2s−2c)

=

2×2×2×2×s(s−a)(s−b)(s−c)

=4

s(s−a)(s−b)(s−c)

.

∴ % change in Area =

A

A

′

−A

×100

=

s(s−a)(s−b)(s−c)

4

s(s−a)(s−b)(s−c)

−

s(s−a)(s−b)(s−c)

×100

=

1

4−1

×100

=300%

Step-by-step explanation:

hope it will help you

Answer 2

Answer:

300%

Step-by-step explanation:

Let the sides of the triangle be a,b,c

and semi perimeter =s

area of triangle=∆=√s(s-a)(s-b)(s-c)

If all the sides are doubled, then

area=√2s(2s-2a)(2s-2b)(2s-2c)

=√16s(s-a)(s-b)(s-c)

=4√s(s-a)(s-b)(s-c)

=4∆

so increase in area=4∆-∆=3∆

so percentage increase in area

=(increase in area/original area)×100%

=(3∆/∆)×100%

=(3×100)%

=300%.