Question

The perimeter of a triangle is 44 cm. Its sides are in the ratio 9:7:6. Find its area. ​

Answer 1

Step-by-step explanation:

Given :-

The perimeter of a triangle is 44 cm. Its sides are in the ratio 9:7:6.

To find :-

Find its area. ?

Solution :-

Given that

The ratio of the three sides of a triangle = 9:7:6

Let they be 9X cm , 7X cm , 6X cm

We know that

Perimeter of a triangle is the sum of the lengths of the three sides

Perimeter of the given triangle

=> P = 9X+7X+6X cm

=> P = 22X cm

According to the given problem

The perimeter of a triangle is 44 cm

=> 22X = 44

=> X = 44/22

=> X = 2 cm

Now,

9X = 9(2) = 18 cm

7X = 7(2) = 14 cm

6X = 6(2) = 12 cm

The three sides of the triangle are 18 cm, 14 cm and 12 cm

We know that

Area of a triangle whose sides are a ,b and c units y Heron's formula ∆ = √[S(S-a)(S-b)(S-c)] sq.units

We have,

a = 18 cm

b = 14 cm

c = 12 cm

Where , S = (a+b+c)/2 = P/2 units

S = 44/2 cm = 22 cm

Now,

Area of the given triangle

=> ∆ = √[22(22-18)(22-14)(22-12)] sq.cm

=> ∆ = √(22×4×8×10) sq.cm

=> ∆ = √(2×11×4×4×2×2×5) sq.cm

=> ∆ = 4×2×√(11×2×5) sq.cm

=> ∆ = 8√110 sq.cm or

=> ∆ = 8× 10.48 sq.cm

=> ∆ = 83.90 sq.cm

Answer:-

The area of the given triangle is 8√110 sq.cm or 83.90 sq.cm

Used formulae:-

→ Perimeter of a triangle is the sum of the lengths of the three sides

→ Area of a triangle whose sides are a ,b and c units y Heron's formula ∆ = √[S(S-a)(S-b)(S-c)] sq.units

→ S = (a+b+c)/2 = P/2 units