Question

The sides of a triangle are x,x+1,2x-1 and its area is x✓10. Find the value of x

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Answer 1

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Answer 2

Answer:

Given,

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

Area of a triangle = x√10 sq. unit

Therefore,

Perimeter of a triangle = x + (x+1) + (2x-1) unit

= x+x+1+2x-1 unit

= 4x unit

Semi-perimeter (s) = Perimeter/2

= 4x/2 unit

= 2x unit

A.T.Q,

Area of a triangle = x√10 sq. unit

or, √{s (s-a) (s-b) (s-c)} = x√10

or, √[2x (2x-x) {2x-(x+1)} {2x-(2x-1)}] = x√10

or, √{2x × x (2x-x-1) (2x-2x+1)} = x√10

or, √{2x^2 × (x-1) × 1} = x√10

or, √(2x^3 - 2x^2) = x√10

squaring both side

or, {√(2x^3 - 2x^2)}^2 = (x√10)^2

or, 2x^3 - 2x^2 = 10x^2

or, 2x^3 - 2x^2 - 10x^2 = 0

or, 2x^3 - 12x^2 = 0

or, 2x^2 (x - 6) = 0

or, (x-6) = 0/2x^2

or, x - 6 = 0

or, x = 6

Answer :- The value of x is 6.