Question

if each side of a triangle is triplet then find the ratio of the area of the new triangle thus formed and the given triangle​

Answer 1

Answer:

Let a,b and c denotes the length of the sides of the triangle.

Area of the triangle, A

1

=

s(s−a)(s−b)(s−c)

, where s is the semi-perimeter of the triangle.

So, semiperimeter s=

2

a+b+c

When the sides of the triangle are doubled, we get

s

′

=

2

2a+2b+2c

=a+b+c=2s, where s

′

is the semi-perimeter of the new triangle

Now, Area of the new triangle, A

2

=

s

′

(s

′

−2a)(s

′

−2b)(s

′

−2c)

=

2s(2s−2a)(2s−2b)(2s−2c)

=

16s(s−a)(s−b)(s−c)

=4

s(s−a)(s−b)(s−c)

=4A

1

So, ratio of the are of new triangle to the given triangle =

A

1

A

2

=

A

1

4A

1

=4:1