Question

Given: ΔABC,

BK⊥AC,

AB = BC = AC= a.

Find: BK, The area of ΔABC

Answer 1

To find the length of BK, we use the Pythagorean theorem: a^2 = b^2 + x^2. The area of triangle ABC can be found using Heron's formula: A = √(s(s-a)(s-b)(s-c))

Step-by-step explanation:

To find the length of BK, we need to use the Pythagorean theorem. Since BK is perpendicular to AC, it forms a right angle. Let's call the length of BK 'b'. Using the Pythagorean theorem, we have:

a^2 = b^2 + x^2

Simplifying this equation, we get:

b^2 = a^2 - x^2

b = √(a^2 - x^2)

To find the area of triangle ABC, we can use Heron's formula. Let's call the area 'A'. Heron's formula states:

A = √(s(s-a)(s-b)(s-c))

Where s is the semi-perimeter of the triangle and can be calculated as:

s = (a + b + c) / 2

So, the area of triangle ABC is A = √(s(s-a)(s-b)(s-c))