Question

sides of triangle are in a ratio 10 19 25 and a perimeter is a area is 540 and find is area​

Answer 1

Answer:

Step-by-step explanation:

Let the sides be 10x , 19x and 25x

Perimeter of a triangle = a + b + c    {a, b and c are sides of a triangle}

540 units = 10x + 19x + 25x

540 = 54x

10 = x    [ a = 10x = 100 , b = 19x = 190 and c = 25x = 250 ]

By Using Heron's formula

Area of a triangle = √s(s-a)(s-b)(s-c)       {s = semi-perimeter}

Area = √270(270-100)(270-190)(270-250)             [ s = 540/2 = 270 ]

Area = √270 × 170 × 80 × 20

Area = √3 × 3 × 3 × 10 × 17 × 10 × 2 × 2 × 2 × 10 × 2 × 10   [By factorizing]

Area = √2 × 2 × 2 × 2 × 10 × 10 × 10 × 10 × 3 × 3 × 3 × 17

Area = 2 × 2 × 10 × 10 × 3 × √3 × 17

Area = 1200√51 units²

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