Question

The sides of a triangle are in the ratio 5:7:8 and its perimeter is 300 cm. Find its area.​

Answer 1

Step-by-step explanation:

5x+7x+8x =300

20x =300

x =300/20

=15

sides , a=5×15 =75cm

b=7×15=105cm

c = 8×15=120

area =

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

$\sqrt{150 \times 75 \times 45 \times 30}$

$\sqrt{2 \times 75 \times 75 \times 15 \times 3 \times 15 \times 2} \\ \\ = 2 \times 75 \times 15 \times \sqrt{3} = 2250 \sqrt{3} cm {}^{2}$

Answer 2

Answer :-

• The area of triangle is 3897.11cm²

Step-by-step explanation:

To Find:-

• The area of triangle

Solution:

Given that,

• The sides of triangle are in the ratio of 5:7:8
• Perimeter of ∆ = 300cm.

∴ The sides of triangle are :-

Firstly, let's consider the sides of triangle, which are in the ratio as 5x, 7x and 8x.

We know,

• Perimeter of ∆ = Sum of three sides.

⇒ 5x + 7x + 8x = 300

⇒ 12x + 8x = 300

⇒ 20x = 300

⇒ x = 300/20

⇒ x = 30/2

⇒ x = 15

The sides are :-

• 5x = 5*15 = 75cm
• 7x = 7*15 = 105cm
• 8x = 8*15 = 120cm

According the question,

Firstly, finding semi-perimeter :-

We know,

• Semi-perimeter of ∆ = ( a + b + c ) / 2

Where,

• a, b and c are the sides of triangle.

⇒ ( a + b + c ) / 2

⇒ ( 75 + 105 + 120 ) / 2

⇒ 300/2

⇒ 150

Now, area of triangle :-

We know,

• Area of ∆ = √s ( s - a ) ( s - b ) ( s - c )

⇒ √s ( s - a ) ( s - b ) ( s - c )

⇒ √ 150 ( 150 - 75 ) ( 150 - 105 ) ( 150 - 120 )

⇒ √ 150 ( 75 ) ( 45 ) ( 30 )

⇒ √ 150 × 75 × 45 × 30

⇒ √ 15187500

⇒ 3897.11cm²