Question

A side of traingl 25:17:12 and its permeter is 540 cm. find its area.​

Answer 1

Step-by-step explanation:

Assumption: Let the sides of the triangle be 25x , 17x and 12x.

Perimeter of the triangle = 540 cm

Therefore,

25x + 17x + 12x = 540

=> 54x = 540

=> x = 10

First side = 25x = 250 cm

Second side = 17x = 170 cm

Third side = 12x = 120 cm

Area :-

Semi - perimeter = 540/2 cm

= 270 cm

Area = √{270×(270 - 250)×(270 - 170)×(270 - 120)} cm²

= √(270×20×100×150) cm²

= √(8,10,00,000) cm²

= 9000 cm²

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Answer 2

$\huge \fbox{\fbox{Question:-}}$

A side of triangle are in this ratio 25:17:12 and it's perimeter is 540cm. Find its area.

$\huge \fbox {\fbox{Answer:-}}$

Given:

• Side of triangle in ratio 25:17:12.
• Perimeter of triangle is 540 cm.

To find:

• Area of triangle.

Formula required:

$\small \bf{•Perimeter \: of \:Triangle = Sum \: of \: all \: sides}$

$\small \bf{•Area \: of \: Triangle = { \sqrt{s(s - a)(s - b)(s - c)}}}$

Where,

• s=semi-perimeter of triangle.
• a,b and c is sides of triangle.

Solution:

We know that,

Perimeter of Triangle=Sum of all sides

∴540cm=25x+17x+12x

∴540cm=54x

∴540/54=x

→x=10cm

Then, semi-perimeter and sides of triangle,

$\small{s = \frac{250 + 170 + 120}{2} = \frac{540}{2} = 270cm}$

a=25x=25×10=250cm;

b=17x=17×10=170cm;

c=12x=12×10=120cm

Hence, sides of triangle are 250cm,170cm and 120cm.

$\bold{Area \: of \: Triangle = \sqrt{s(s - a)(s - b)(s - c)}}$

$\sf{∴Area \: of \: Triangle = \sqrt{270(270 - 250)(270 - 170)(270 - 120)}}$

$\sf{∴Area \: of \: Triangle = \sqrt{270 \times 20 \times 100 \times 150}}$

∴Area of Triangle=√8,10,00,000

∴Area of Triangle=9,000cm²

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