Question

In a right triangle the length of a hypotenuse is c and the length of one leg is a, and the length of the other leg is b, what is the value of b, if a=2 (root of)3 and c=2b

Answer 1

The value of b in the right triangle is √6.

Step-by-step explanation:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is written as:

a² + b² = c²

In this case, we are given that a = 2√3 and c = 2b. To find the value of b, we can substitute the given values into the equation and solve for b:

(2√3)² + b² = (2b)²

12 + b² = 4b²

3b² - b² = 12

2b² = 12

b² = 6

b = √6

Therefore, the value of b is √6.

Answer 2

Use the Pythagorean Theorem.

c^2 = a^2 + b^2. Thus, (2b)^2 = (2√3)^2 + b^2

Simplifying, we get: 4b^2 = 4(3) + b^2, or 3b^2 = 4(3). Then b^2 = 4, and b = +2