Question

Assertion : The sides of a triangle are in the ratio of 25: 14:12 and its perimeter is 510 cm. Then the area of the triangle is 4449.08 cm? Reason : Perimeter of a triangle = a + b + C, where a, b, c are sides of a triangle.​

Answer 1

Assertion:

True

Proof:

Let say the sides are 25x, 14x and 12x

A/q,

=>> Perimeter of the triangle = 510

=>> 25x + 14x + 12x = 510

=>> 51x = 510

=>> x = 510/51

=>> x = 10

Therefore, Actual sides are

• 25x = 250
• 14x = 140
• 12x = 120

Semi-perimeter is:-

=>> ½ of 510

=>> 255

By heron's formula,

=>> √s(s - a)(s - b)(s - c)

=>> √255(255 - 250)(255 - 140)(255 - 120)

=>> √255(5)(115)(135)

=>> 4449.08cm² (approx.)

Answer 2

Given: The sides of a triangle are in the ratio of 25: 14:12 and its perimeter is 510 cm.

To find: Proof that the area of the triangle is 4449.08 cm²

Solution: Let the sides of the triangle be 25x, 14x and 12x respectively.

Now according to the question,

25x + 14x + 12x = 510

⇒ 51x = 510

⇒ x = 510/51

⇒ x = 10

Therefore, the sides of the triangle:

25 × 10 = 250 cm

14 × 10 = 140 cm

12 × 10 = 120 cm.

The semi-perimeter of the triangle = 510/2 cm = 255 cm.

Therefore, the area of the triangle

= √(s×(s-a)×(s-b)×(s-c))

= √(255×(255-250)×(255-140)×(255-120))

= √(255 × 5 × 115 × 135)

= 4449.08 cm²

Hence, proved.