Question

A triangle has 3 sides which are
$(10x + 12) \: and \: 7 {x}^{2} + 10x + 13 \: and \: 5 {x}^{2} + 5x - 2$
find the perimeter of the triangle
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Answer 1

Answer:

If a,b,c are the sides of a triangle , then according to Hero's Formula area of triangle is

s(s−a)(s−b)(s−c)

where s=

2

a+b+c

For the given triangle,

s=

2

x+x+1+2x−1

=

2

4x

=2x

Area =x

10

2x(2x−x)(2x−x−1)(2x−2x+1)

=x

10

2x(x)(x−1)(1)

=x

10

x

2(x−1)

=x

10

2(x−1)

=

10

⇒2(x−1)=10

x−1=5

x=6