Question

sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm.
$\large{ \red{\: find \: its \: area.}}$
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Answer 1

Step-by-step explanation:

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Answer 2

Given-

• Sides of a triangle are in ratio 12:17:25
• Perimeter of the triangle is 540cm.

Need to find-

• Area of the traingle

$\huge{ \mathtt{ \purple{SOLUTION:-}}}$

Let the three sides of the traingle be 12x,17x and 25x.

Therefore,

a =12x

b =17x

c =25x

Perimeter of the triangle= 540cm

$\large{ \implies{a + b + c = 540cm}} \\ \large{ \implies{12x + 17x + 25x = 540cm}} \\ \large{ \implies{54x = 540cm}}$ $\large{ \implies{x = \frac{540}{54} cm}} \\ \large{ \implies{x = 10}}$

Therefore,

Sides of the triangle are-

a = 10×12 =120cm

b = 10×17 =170cm

c = 25×10 =250cm

Area of the ∆ -

$\small{ \implies{ \sqrt{s(s - a)(s - b)(s - c)}}} \\ \small{ \implies{ \sqrt{270(270 - 120)(270 - 170)(270 - 250)}}}$

$\small{ \implies{ \sqrt{270(150)(100)(20)}}}$

$\small{ \implies{ \sqrt{81000000}}}$

$\small{\bold{ \implies{area = 9000 {cm}^{2} }}}$

Therefore,

$\small{\boxed{\blue{Area = 9000 {cm}^{2} }}}$