Question

The sides of a triangle are in the ratio of 12:17:25.
the perimeter is 540cm .
Find the area of the triangle using Heron's formula

Answer 1

Answer:

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Answer 2

Answer:

Area of the triangle =

$9000 {cm}^{2}$

Step-by-step explanation:

Let the sides of the triangle ABC be 12x, 17x and 25x where x is their common factor.

ATQ,

A + B + C = 540cm

=> 12x + 17x + 25x = 540cm

=> 54x = 540cm

=> x = 540/54 = 10cm

so the sides are -

12x = 12(10) = 120cm

17x = 17(10) = 170cm

25x = 25(10) = 250cm

Now, S = A+B+C/2 = 540/2 = 270

Heron's formula -

Area of the triangle =

$\sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{270(270 - 120)(270 - 170)(270 - 250)} \\ = \sqrt{270 \times 150 \times 100 \times 20} \\ = \sqrt{81000000} \\ = 9000 {cm}^{2}$