Assertion: The sides of a triangle are in the ratio of 25: 14: 12 and its perimeter is 510 m. Then the greatest side is 250 m. Reason: Perimeter of a triangle = a+b+c, where a, b, c are sides of a triangle
which of the option is correct........
(a) Both assertion and reason are true and reason is the correct explanation of assertion.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion.
(c) Assertion is true but reason is false.
(d) Assertion is false but reason is true.

Assertion: The sides of a triangle are in the ratio of 25: 14: 12 and its perimeter is 510 m. As far as we know, the information provided is true since it is given to us in the problem.

Let x be the common factor for the sides. Then, the sides are 25x, 14x, and 12x.

The Assertion is TRUE

Reason:

"Then the greatest side is 250m" is also true since:

"Perimeter of a triangle = a+b+c, where a, b, c are sides of a triangle"

From above, we can enter the sides and set them equal to 510m:

25x + 14x + 12x = 510m

Solving for x gives x = 10. Therefore, the sides are 250m, 140m, and 120m. The longest side is 250m,

The Reason is also TRUE:

The reason directly explains why the assertion is true. By knowing the formula for the perimeter and the ratio of the sides, we can calculate the individual side lengths and confirm that the largest side is 250m.

Therefore, both the assertion and the reason are true, and the reason accurately explains why the assertion holds.