Question

The perimeter of a triangle is 54 cm and its sides are in the ratio 5:6:7 , find the area of triangle​

Answer 1

Step-by-step explanation:

Ratio = 5 : 6 : 7

sum of sides = perimeter = 18

side, 518×54=15

618×54=18

718×54=21 metres

S=15+18+212=27

Area of △=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

=27×12×9×6−−−−−−−−−−−−√=546–√m2

Answer 2

☆ Solution ☆

Given :-

• The perimeter of a triangle is 54 cm.
• The sides of triangle are in the ratio 5:6:7.

To Find :-

• The area of triangle.

Step-by-Step-Explaination :-

Let the ratios be 5x, 6x and 7x

According to the condition,

5x + 6x + 7x = 54

18x = 54

x = 54/18

x = 3

Thus,

The value of x is 3 cm

So,

5x = 5 × 3 = 15 cm

6x = 6 × 3 = 18 cm

7x = 7 × 3 = 21 cm

Now,

By using heron's formula :-

As we know that :-

S = a + b + c/2

Where,

• a = 15

• b = 18

• c = 21

Putting the respective value,

S = 15 + 18 + 21/2

S = 54/2

S = 27

Hence,

Side = 27 cm

Now,

Area of triangle = √ s ( s - a ) ( s - b ) ( s - c )

Where,

• S = 27

• a = 15

• b = 18

• c = 21

Putting the respective value,

Area of triangle = √ 27 ( 27 - 15 ) ( 27 - 18 ) ( 27 - 21 )

Area of triangle = √ 27 ( 12 ) ( 9 ) ( 6 )

Area of triangle = √ 3 × 3 × 3 × 2 × 2 × 3 × 3 × 3 × 2 × 3

Area of triangle = 3 × 3 × 3 × 2√6

Area of triangle = 54√6 cm²

Hence,

Area of triangle = 54√6 cm²