Question

sides of a triangle are in the ratio of 12: 17 : 25 and it's perimeter is 540cm. Find the area of the triangle. (By using heron's formula)​

Answer 1

Answer:

It is given that sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. We have found that its area is 9000 cm2.

Answer 2

⚘ Question:

Sides of a triangle are in the ratio of 12: 17 : 25 and the perimeter is 540cm. Find the area of the triangle. (By using heron's formula)

⚘ Answer:

Let the sides be 12x, 17x and 25x.

Perimeter = 540cm

Perimeter = (Sum of all sides) a+b+c

${\longmapsto} \: {\mathrm{540 = 12x + 17x + 25x}}$

${\longmapsto} \: {\mathrm{540 = 54x}}$

${\longmapsto} \: {\mathrm{x = \frac{540}{54} }} \\ {\longmapsto} \: {\mathrm{x = 10}}$

• Sides of the triangle =

${\rightarrow} \: {\mathrm{a = 12x = 12 \times 10 = 120cm}}$

${\rightarrow} \: {\mathrm{b = 17x = 17 \times 10 = 170cm}}$

${\rightarrow} \: {\mathrm{c = 25x = 25 \times 10 = 250cm}}$

${\mathrm{S = \frac{Perimeter}{2} = \frac{540}{2} = 270cm}}$

⚘ Area of triangle =

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

${\tt{(s - a) = 270 - 120 = 150}} \\ {\tt{(s - b) = 270 - 170 = 100}} \\ {\tt{(s - c )= 270 - 250 = 20}}$

${\tt{ = \sqrt{270 \times 150 \times 100 \times 20} }} \\ {\tt{ = 3 \times 3 \times 10 \times 10 \times 5 \times 2}} \\ {\tt{ = 9 \times 1000 = {\blue{9000 {cm}^{2}} }}}$

Therefore, area of the triangle = 9000cm²