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

Question

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

in progress 0
2 months 2021-11-23T04:40:50+00:00 2 Answers 0 views 0

• Area of the triangle is 135√7 units.

Given:–

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

ToFind:–

• 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

1357 units

_____________________

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