Question

5. Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. find its area using heron formula​.​

Answer 1

Answer:

9000 cm²

Step-by-step explanation:

Given,

Sides of a triangle are in the ratio :- 12 : 17 : 25

Perimeter of the triangle = 540 cm

To Find :-

Area of the triangle by using heron's formula.

How To Do :-

As they given the value of sides in the form of ratios we need to take a constant and we need to assume those values by taking the constant. We need add all the value of sides and we need to equate its to value perimeter. The we will get the values of sides of the triangle. The we need to find the semi perimeter and we need to apply heron's formula to get the value of the area of the triangle.

Formula Required :-

Heron's formula :-

If 's' is semi - perimeter and a , b , c are the lengths of sides of a triangle then :-

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

Solution :-

Sides of the triangle = 12 : 17 : 25

Let , a , b , c are the sides of the triangle :-

→ a : b : c = 12 : 17 : 25

Let,

a = 12x , b = 17x , c = 25x

→ 12x + 17x + 25x = 540cm

54x = 540cm

x = 540cm/54

x = 10cm

→a =  12x = 12 × 10cm = 120cm

b = 17x = 17 × 10cm = 170cm

c = 25x = 25 × 10cm = 250cm

Semi - perimeter = Perimeter /2

= 540cm/2

∴ s= 270cm

Substituting in heron's formula :-

$Area=\sqrt{270(270-120)(270-170)(270-250)}$

$=\sqrt{270(150)(100)(20)}$

$=\sqrt{270(300000)}$

$=\sqrt{81000000}$

$=\sqrt{81\times 10^6}$

$=\sqrt{9^2\times (10^3)^2}$

$=(\sqrt{9\times 10^3})^2$

= 9 × 10³

= 9000 cm²

∴ Area of the triangle = 9000cm²