Question

side of a triang are in the ratio of 12:7:25 and it's perimeter is 540cm find its area
.​

Answer 1

Question:-

Side of a triangle are in the ratio of 12:7:25 and its perimeter is 540 cm Find its area.

Answer:-

Given,

$\implies$ Side of a triangle are in the ratio of 12:7:25

$\implies$ Perimeter of a triangle = 540cm

To Find,

$\implies$ Area of Triangle.

Calculations,

Let,

Common ratio = X

According to the question,

Sides of the triangle = 12x :7x :25x

$\implies$ 12x + 7x +25x = 540cm

$\implies$ 44x = 540cm

$\implies$ X = $\dfrac{540cm}{44}$

$\implies$ X = 12cm

Sides of Triangles,

a = 12 × 12 = 144

b = 7 × 12 = 84

C = 25 × 12 = 300

Now,

2s = 540

$\implies$ S = $\dfrac{540}{2}$

$\implies$ S = 270 cm

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

$\sqrt{270(270-144)(270-78)(270-300)}{cm}^{2}$

$\implies$ $\sqrt{270×126× 192×(-30)}$

$\implies$ $\sqrt{6531840(-30)}$

A = ${9000cm}^{2}$

Area of triangle is 9000cm^2

Answer 2

$\green{\textbf{\underline{\underline{According\:to\:the\:Question}}} </p><p> }$

Ratio of the sides of the triangle

= 12 : 17 : 25

★Assumption

★Ratio be p

★Sides are 12p, 17p and 25p

$\blue{\large{\fbox{Perimeter\;of\;the\;triangle= 540cm}} }</p><p>$

12p + 17p + 25p = 540 cm

⇒ 54p = 540 cm

${\boxed{\sf\:{p=\dfrac{540}{54}}}} </p><p></p><p>$

⇒ P = 10

$\red{\fbox{Sides\;of\;triangle\;are} }$

★12p = 12 × 10

= 120 cm

★17p = 17 × 10

= 170 cm

★25p = 25 × 10

= 250 cm

$\orange{\fbox{Semi\;Perimeter :-} }</p><p>$

$</p><p> \gray{\tt{s=\dfrac{540}{2}}}$

= 270 cm

$\blue{ \large{\fbox{Using\;Herons\;Formula}} </p><p>}</p><p>$

$\green{\tt{\sqrt{s(s-a)(s-b)(s-c)}}}</p><p></p><p>$

$\orange{\tt{\sqrt{270(270-120)(270-170)(270-250)}}}</p><p>$

$\blue{\tt{\sqrt{270\times 150\times 100\times 20}}</p><p> }$

= 9000 cm²

$\pink{\boxed{\sf\:{Hence\;we\;get\;Area=9000\;cm^2}}}$