Question

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

Answer 1

$\huge\bf\underline{Answer}$

The sides of the triangle are 18 cm, 14 cm and 12 cm. The area of the triangle is 8√110 cm² respectively.

Solution:-

Given,

Ratio of three sides = 9:7:6

Perimeter of the triangle = 44 cm

Let the three sides of the triangle be 9x, 7x and 6x

As we know that the formula of the perimeter of triangle is :-

Perimeter = a + b + c

(where a , b and c are the sides of the triangle)

According to question,

=> 9x + 7x + 6x = 44

=> 22x = 44

=> x = 44/22

=> x = 2

Hence, the value of x is 2.

Therefore,

The first side => 9x = 9 × 2 = 18 cm

The second side => 7x = 7 × 2 = 14 cm

And the third side => 6x = 6 × 2 = 12 cm

Now,

(From the following sides, we can guess that it's a scalene triangle)

Therefore,

Semi- perimeter => Perimeter/2 = 44/2 = 22 cm

Area of scalene triangle= √s(s - a)(s - b)(s - c) sq.unit

= √22(22 - 18)(22 - 14)(22 - 12) cm²

= √22 × 4 × 8 × 10 cm²

= √2 × 11 × 2 × 2 × 2 × 2 × 2 × 2 × 5 cm²

= 2 × 2 × 2 √11 × 2 × 5 cm²

= 8√110 cm²

Hence, the area of the triangle is 8√110 cm²

Answer 2

Answer:

83.2 cm² (approx)

Step-by-step explanation:

Let the common ratio be x.

P = 9x+7x+6x

44=22x

x = 2

1st side=9x = 9(2) = 18cm

2nd side = 7x = 7(2) = 14cm

3rd side = 6x = 6(2) = 12cm

s = P/2

= 44/2

= 22 cm

AREA= √{s(s-a)(s-b)(s-c)}

= √{22(22-18)(22-14)(22-12)}

= √{22(4)(8)(10)}

= 8 × √110

= 8√110

= 8 × 10.4 (approx)

= 83.2 cm² (approx)

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