Question

perimeter of a triangle is 540 m and its sides are in the ratio 12 : 25 : 17. Find the area
of the triangle.
Show the steps.

Answer 1

Let the sides of the triangle be 12a,25a,17a.

We know that perimeter of the triangle = Sum of all sides $$

⇒12a+25a+17a=54a

Given, perimeter of the triangle =540m

⇒54a=540m

a=10m

So, the lengths of the sides of triangle are

12a=120m

25a=250m

17a=170m

We can use Heron's formula to get the area of triangle

Area of triangle with sides with sides a,b,c and semiperimeter s=

s(s−a)(s−b)(s−c)

.

and s=

2

a+b+c

For triangle with sides 120 m, 250 m and 170 m,

s=

2

120+250+170

=270m

Substituting the sides 120 m, 250 m and 170 m in the Heron's formula, we get

270(270−120)(270−250)(270−170)

=

270×150×20×100

=

9×30×30×5×20×20×5

=3×30×5×20

=9000m

2

Answer 2

Answer:

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