Assertion: The altitude p of an equilateral triangle having each side a is given by 𝑝 = √32 𝑎.Reason: If p is the altitude of an equilateral triangle, then its area A is given by ∆= 𝑝2√3

The assertion and the reason are not correctly related. Here's why:

Assertion: The altitude (p) of an equilateral triangle with each side (a) is given by p = √3/2 * a. This is because in an equilateral triangle, the altitude splits the base into two equal parts, forming two 30-60-90 right triangles. The ratio of the sides in a 30-60-90 triangle is 1:√3:2. Therefore, the altitude (the side opposite the 60-degree angle) is √3/2 times the length of the side of the equilateral triangle.

Reason: The area (A) of a triangle is given by A = 1/2 * base * height. In an equilateral triangle, the base is a and the height is the altitude p. Therefore, the area of an equilateral triangle is A = 1/2 * a * p. However, this formula does not directly give us p = √3/2 * a. Instead, if we substitute p = √3/2 * a into the formula for the area of a triangle, we get A = 1/2 * a * √3/2 * a = √3/4 * a^2, which is the formula for the area of an equilateral triangle.

So, the assertion is correct but the reason is not directly related to the assertion. The reason is a general formula for the area of a triangle, not a derivation of the formula for the altitude of an equilateral triangle.