Question

Side of the triangle are in the ratio of 12:17:25 and its perimeter is 54 cm.Find the area

Answer 1

GIVEN :-

ratio between the sides of the triangle is 12 : 17 : 25

perimeter of the triangle = 54cm

➡ it's semi-perimeter = 54/2 = 27cm

let the sides of the triangle be 12x, 17x and 25x respectively.

we know that, sum of all sides = 54cm

➡ 12x + 17x + 25x = 54cm

➡ 54x = 54cm

➡ x = 54/54

➡ x = 1cm

therefore, the sides are :-

• 12x = 12 × 1 = 12cm

• 17x = 17 × 1 = 17cm

• 25x = 25 × 1 = 25cm

area of the triangle using heron's formula = √s(s - a)(s - b)(s - c)

where s is the semi-perimeter of the triangle and a, b and c are it's sides respectively.

= √[27(27 - 12)(27 - 17)(27 - 25)]

= √(27 × 15 × 10 × 2)

= √(3 × 3 × 3 × 3 × 5 × 2 × 5 × 2)

= √(2 × 2 × 3 × 3 × 3 × 3 × 5 × 5)

= 2 × 3 × 3 × 5

= 90cm²

hence, the area of the triangle is 90cm²

Answer 2

Answer:

Let the first side of triangle = 12x

Let the second side of triangle = 17x

Let the third side of triangle = 25 x

____________________

Perimeter = 54 cm

A.T.Q

12x + 17x + 25x = 54

54x = 54

x = 54/54

x = 1

Puting the value of x.

So, the first side = 12x = 12(1) = 12 cm

Second side = 17x = 17(1) = 17 cm

Third side = 25x = 25(1) = 25 cm

____________________

Now, by using heron's formula

Semi perimeter = 54/2

s = 27 cm

√27(27 - 12)(27 - 17)(27 - 25)

√27 * 15 * 10 * 2

√3 * 3 * 3 * 3 * 5 * 5 * 2 * 2

90 cm²

Hence , area of triangle = 90 cm²