Question

The sides of the triangle are x cm,x+1 cm, and 2x-1 cm. Its area is x root/10 square cm. Find the value

​

Answer 1

Answer:

Sides of triangle are x, x+1, 2x-1

Area of triangle is x \sqrt{10}x

10

To find out:- Value of x

We Know That,

Semi-Perimeter(S)= Perimeter/2

=x+x+1+2x-1/2

=4x/2

=2x

Area Of Triangle= \sqrt{s(s-a)(s-b)(s-c)}

s(s−a)(s−b)(s−c)

or, x \sqrt{10}x

10

=\sqrt{2x(2x-x)(2x-x-1)(2x-2x+1)}

2x(2x−x)(2x−x−1)(2x−2x+1)

or, x \sqrt{10} =[tex] \sqrt{2x.x(x-1).1}x

10

=[tex]

2x.x(x−1).1

or, x \sqrt{10} =[tex] \sqrt{2x^2(x-1)}x

10

=[tex]

2x

2

(x−1)

or, x \sqrt{10} =[tex]x\sqrt{2(x-1)}x

10

=[tex]x

2(x−1)

Squaring Both Sides, We get

or, 10=2(x-1)

or, 10=2x-2

or, 10+2=2x

or, 12/2 = x

or, 6 = x

Therefore, x = 6

hence, The value of X is 6 Ans..

Step-by-step explanation:

mark me as brainlist

Answer 2

Answer:

x is 6

Step-by-step explanation:

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