Question

The sides of a triangle are in the ratio of 3 : 5 : 7 and its perimeter is 300 cm.Its area will be:

Answer 1

Answer:

1500√3cm2

Step-by-step explanation:

Define x:

Ratio = 3 : 5 : 7

Let x be the constant ratio

Ratio = 3x : 5x : 7x

Find the lengths:

3x + 5x + 7x = 15x

15x = 300

x = 20

3x = 3(20) = 60 m

5x = 5(20) = 100 m

7x = 7(20) = 140 m

Find the area;

Area = √p(p - a)(p - b) (p - c)

p = 300 ÷ 2 = 150

Area = √150(150 - 60) ( 150 - 100)(150 - 140)

Area = √6750000

Area = 1500√3 m²

Answer: The area of the triangle is 1500√3 m²

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Answer 2

Answer:

2,598.076cm² (or) 1500√3cm²

Step-by-step explanation:

Given:

Ratio of sides of triangle = 3:5:7

Perimeter of triangle = 300cm

To Find:

Area of the triangle

Assumption:

Let the sides of triangle be 3x , 5x and 7x

Formulas Used:

Perimeter of triangle = sum of all its sides

Area of triangle =

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

where s = Semi-perimeter of triangle

Solution:

￫ 3x + 5x + 7x = 300cm

=> 15x = 300cm

=> x = 300cm/15

=> x = 20cm

1st side = 3x = 3×20cm = 60cm

2nd side = 5x = 5×20cm = 100cm

3rd side = 7x = 7×20cm = 140cm

￫ Semi-perimeter = 300cm/2 = 150cm

Area of triangle =

$\sqrt{{150(150 - 60)(150 - 100)( 150 - 140)}}$

$= \sqrt{150 \times 90 \times50 \times 10 }$

$= \sqrt{6,750,000}$

$= 2,598.076 {cm}^{2}$

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