Question

Given the right triangle ABC, if segment AC is 3√6, then AB = ______.

3√4

3√3

4√3

3√7

Answer 1

AB = 3√3

Explanation:

ABC is a 45 45 90 right triangle

Ratio of leg : hypo = a :a√2 (a = leg)

Given hypo AC = 3√6

So AB = BC = 3√6 / √2 = 3√3

Answer 2

Option B is correct

`3√(3)`

Explanation:

Definition: 45-45-90 triangle

In a 45-45-90 triangle, the length of hypotenuse is
`√(2)` times the length of leg.

As per the statement:

Given the right triangle ABC, if segment AC is 3√6

⇒
`\text{Hypotenuse side} = AC = 3√(6)` units

Since, the given triangle is 45-45-90 triangle

⇒AB=BC

Let x be the side of length of leg.

then;

by definition we have;

Length of hypotenuse is
`√(2)` times the length of leg.

⇒
`3√(6) = √(2)x`

Divide both side by
`√(2)` we have;

`(3√(6))/(√(2)) = x`

⇒
`(3 \cdot √(2) \cdot √(3))/(√(2))= x`

Simplify:

`x = 3√(3)`

therefore, the length of side AB is,
`3√(3)` units