Question

Solve the following question : The length of sides of a triangle are in the ratio 4:5:6 and its perimeter is 180 cm find the area of the triangle. (Use Heron's formula)​

Answer 1

Explanation:

now add all the side again 48cm+60cm+72=180cm

Answer 2

Given data : The length of the sides of a triangle are in the ratio 4:5:6 abd perimeter of the triangle is 180 cm.

Solution : Let the length of sides be 4x, 5x and 6x.

Now, a/c to given data,

➜ Perimeter of the triangle = a + b + c

Where, a = 4x, b = 5x and c = 6x

➜ 180 = 4x + 5x + 6x

➜ 180 = 9x + 6x

➜ 180 = 15x

➜ x = 180/15

➜ x = 12

Now,

➜ a = 4x = 4 * 12 = 48 cm

➜ b = 5x = 5 * 12 = 60 cm

➜ c = 6x = 6 * 12 = 72 cm

Now, to find out area of the triangle, we use Heron's formula;

➜ semi-perimeter, s = {a + b + c}/2

➜ semi-perimeter, s = {48 + 60 + 72}/2

➜ semi-perimeter, s = {108 + 72}/2

➜ semi-perimeter, s = 180/2

➜ semi-perimeter, s = 90 cm

Now,

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

➜ Area of triangle = √{90 (90 - 48) (90 - 60) (90 - 72)}

➜ Area of triangle = √{90 * 42 * 30 * 18}

➜ Area of triangle = √{3780 * 540}

➜ Area of triangle = √{2041200}

➜ Area of triangle = 1428.7057 cm²

Answer : Hence area of the triangle is 1428.7057 cm².

{Note :

➜ Semi-perimeter, S = {Perimeter of triangle}/2

➜ Semi-perimeter, S = {180}/2

➜ Semi-perimeter, S = 90 cm}