Question

3. If sides
of the triangle are in the
ratio 6:4:5 and its perimeter is
90 on then find the area?​

Answer 1

Answer:  357.17 unit sq.

Step-by-step explanation:Since the ratio is 6:4:5 , let the sides be 6x , 4x and 5x .

therefore, 6x + 4x + 5x = 90

               15x = 90

                  x = 90÷15

                  x = 6

sides are 36 , 24  and 30

after finding the sides we will find the area by using the heron's formula

area = √s(s-a)(s-b)(s-c)

where s = perimeter/2

area = √(45)(45-36)(45-24)(45-30)

        = √45×9×21×15

         = 45×3√7

         = 135×2.645

         = 357.17

Answer 2

AnswEr :-

• Area of the triangle is 135√7 units.

Given :-

• Sides of a triangle are in ratio 6:4:5.

To Find :-

• Area of the triangle.

SoluTion :-

Sides of the triangle are in ratio 6:4:5

Put x in the ratio

Then,

Sides are 6x , 4x , 5x

Perimeter of a triangle = sum of all sides.

★According to the question

» 6x + 4x + 5x = 90

→ 15x = 90

→ x = 90/15

→ x = 6

Put the value of x in the ratio.

6x = 6 × 6 = 36

4x = 4 × 6 = 24

5x = 5 × 6 = 30

Here,

• a = 36

• b = 24

• c = 30

We've to find semi - perimeter of the triangle.

★ Formula for finding semi - perimeter ( S ) of the triangle is

» S = a + b + c / 2

→ S = 36 + 24 + 30 / 2

→ S = 90/2

→ S = 45

★ Formula for finding area of the triangle is

» √s (s - a) (s - b) (s - c)

→ √45 (45 - 36) (45 - 24) (45 - 30)

→ √45 × 9 × 21 × 15

→ 135√7 units

Hence, the area of the triangle is 135 units.

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