Question

What is the value of X? We’ve your answer in simplest radical form. 3√2. 2√3 . √2. √6

Answer 1

x = 3
`√(2)`

Explanation:

using Pythagoras' identity in the right triangle

c² = a² + b²

a, b are the legs and c is the hypotenuse

here a = b = 3 and c = x , then

x² = 3² + 3² = 9 + 9 = 18 ( take square root of both sides )

`√(x^2)` =
`√(18)` =
`√(9(2))` =
`√(9)` ×
`√(2)`

x = 3
`√(2)`

Answer 2

x = 3√2

Explanation:

As the legs of the given right triangle are congruent, this is an isosceles right triangle.

In an isosceles right triangle, the two legs are congruent (of equal length), and the ratio of the lengths of the legs to the length of the hypotenuse is 1 : 1: √2. In other words, the hypotenuse is √2 times the length of a leg.

Therefore, if the legs are 3 units in the length, the hypotenuse must be 3√2 units long. So:

`\Large\boxed{\boxed{x = 3√(2)}}`