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

Given :-

Ratio of sides of a triangle = 3 : 5 : 7

Perimeter of the triangle = 300 cm

To Find :-

The area of the triangle.

Analysis :-

Consider the common ratio as a variable.

Multiply that variable to each side.

Make an equation accordingly and find the value of the variable and substitute it in the sides.

Find the semi perimeter accordingly and substitute the values using the Heron's formula.

Solution :-

We know that,

• a = Area
• p = Perimeter
• s = Sides

Let the common ratio be 'x'. Then the sides would be 3x, 5x and 7x.

Given, perimeter = 300 cm

Making an equation,

3x + 5x + 7x = 300

15x = 300

x = 300/15

x = 20

By substituting,

3x = 3 × 20 = 60

5x = 5 × 20 = 100

7x = 7 × 20 = 140

Therefore, the sides are 60 cm, 100 cm and 140 cm.

By the formula,

$\underline{\boxed{\sf Semi \ perimeter=\dfrac{Perimeter}{2} }}$

Substituting them,

Semi perimeter = 300/2 = 150 cm

Using Heron's formula,

$\underline{\boxed{\sf Heron's \ formula=\sqrt{s(s-a)(s-b)(s-c) } }}$

Substituting their values,

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

$\sf =\sqrt{150 \times 90 \times 50 \times 10}$

$\sf =\sqrt{5 \times 3 \times 10 \times 3 \times 3 \times 10 \times 5 \times 10 \times 10 }$

$\sf =100 \times 5 \times 3\sqrt{3}$

$\sf =1500\sqrt{3} \ m^2$

Therefore, the area of the triangle is 1500√3 m².

Answer 2

Answer:

hope it is help ful to you

Step-by-step explanation:

Given :-

Ratio of sides of a triangle = 3 : 5 : 7

Perimeter of the triangle = 300 cm

To Find :-

The area of the triangle.

Analysis :-

Consider the common ratio as a variable.

Multiply that variable to each side.

Make an equation accordingly and find the value of the variable and substitute it in the sides.

Find the semi perimeter accordingly and substitute the values using the Heron's formula.

Solution :-

We know that,

a = Area

p = Perimeter

s = Sides

Let the common ratio be 'x'. Then the sides would be 3x, 5x and 7x.

Given, perimeter = 300 cm

Making an equation,

3x + 5x + 7x = 300

15x = 300

x = 300/15

x = 20

By substituting,

3x = 3 × 20 = 60

5x = 5 × 20 = 100

7x = 7 × 20 = 140

Therefore, the sides are 60 cm, 100 cm and 140 cm.

By the formula,

\underline{\boxed{\sf Semi \ perimeter=\dfrac{Perimeter}{2} }}

Semi perimeter=

2

Perimeter

Substituting them,

Semi perimeter = 300/2 = 150 cm

Using Heron's formula,

\underline{\boxed{\sf Heron's \ formula=\sqrt{s(s-a)(s-b)(s-c) } }}

Heron

′

s formula=

s(s−a)(s−b)(s−c)

Substituting their values,

\sf=\sqrt{150(150-60)(150-100)(150-140)}=

150(150−60)(150−100)(150−140)

\sf =\sqrt{150 \times 90 \times 50 \times 10}=

150×90×50×10

\sf =\sqrt{5 \times 3 \times 10 \times 3 \times 3 \times 10 \times 5 \times 10 \times 10 }=

5×3×10×3×3×10×5×10×10

\sf =100 \times 5 \times 3\sqrt{3}=100×5×3

3

\sf =1500\sqrt{3} \ m^2=1500

3

m

2

Therefore, the area of the triangle is 1500√3 m².