Question

sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. find its area​

Answer 1

Given that ,

" Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. We need to find its area​ "

Let the sides of the triangle be " 12 x " , " 17 x " , " 25 x "

Since perimeter of the triangle is 540 m

⇒ 12 x + 17 x + 25 x = 540

⇒ 54 x = 540

⇒ x = 10 m

So , sides of the triangle are ,

12 x = 12 * 10 = 120 m

⇒ a = 120 m

17 x = 17 * 10 = 170 m

⇒ b = 170 m

25 x = 25 * 10 = 250 m

⇒ c = 250 m

Now , we need to find the area of the triangle .

Use Heron's Formula to find area of triangle . Because , base and height of the triangle are unknown .

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

where , $\bf s=\dfrac{a+b+c}{2}$

$\implies \bf s=\dfrac{120+170+250}{2}\\\\\implies \bf s=\dfrac{540}{2}\\\\\implies \bf s=270\ m$

Now ,

$\bf Area=\sqrt{s(s-a)(s-b)(s-c)}\\\\\implies \bf Area=\sqrt{270(270-120)(270-170)(270-250)}\\\\\implies \bf Area=\sqrt{270(150)(100)(20)}\\\\\implies \bf Area=\sqrt{27*3}*\sqrt{10^6}\\\\\implies \bf Area = 9*10^3\\\\\implies \bf Area=9000\ sq.meters$

So , Area of the triangle is 9000 m²

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \red{Question:-}}}}}}$

Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its Area ...

${ \huge{ \bold{ \underline{ \underline{ \pink{Answer:-}}}}}}$

Given : -

• Sides of Triangle = 12 : 17 : 25
• Perimeter of Triangle = 540 cm

To Find : -

• Area of Triangle = ?

Let : -

• 1st Side = 12x
• 2nd Side = 17x
• 2rd Side = 25x

${ \large{ \bold{ \underline{ \underline{ \orange{According\:to\:the\:Question:-}}}}}}$

$\dashrightarrow\sf{12x+17x+25x=540}$

$\dashrightarrow\sf{54x=540}$

$\dashrightarrow\sf{x=\cancel\dfrac{540}{54}}$

$\dashrightarrow\sf{{ \large{ \bold{ \bold{ \bold{ \purple{x=10}}}}}}}$

Now, : -

$\dashrightarrow\sf{1st\:Side=12(10)}$

$\dashrightarrow\sf{120cm}$

$\dashrightarrow\sf{2nd\:Side=17(10)}$

$\dashrightarrow\sf{170cm}$

$\dashrightarrow\sf{3rd\:Side=25(10)}$

$\dashrightarrow\sf{250cm}$

$\dashrightarrow\sf{s=\dfrac{a+b+c}{2}=\dfrac{120+170+250}{2}=\cancel\dfrac{540}{21}}$

$\dashrightarrow\sf{s=270cm.}$

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

$\dashrightarrow\sf{\sqrt{270(270-120)(270-170)(270-250)}}$

$\dashrightarrow\sf{\sqrt{270\times{150}\times{100}\times{20}}}$

$\dashrightarrow\sf{\sqrt{3\times{3}\times{3}\times{2}\times{5}\times{3}\times{5}\times{2}\times{5}\times{5}\times{5}\times{2}\times{2}\times{2}\times{2}\times{5}}}$

$\dashrightarrow\sf{3\times{3}\times{2}\times{5}\times{5}\times{2}\times{2}}$

$\dashrightarrow\sf{{ \large{ \bold{ \underline{ \underline{ \purple{9000{cm}^{2}}}}}}}}$