Question

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

Answer 1

Answer:

Option B is correct

$3\sqrt{3}$

Step-by-step explanation:

Definition: 45-45-90 triangle

In a 45-45-90 triangle, the length of hypotenuse is $\sqrt{2}$ times the length of leg.

As per the statement:

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

⇒$\text{Hypotenuse side} = AC = 3\sqrt{6}$ 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 $\sqrt{2}$ times the length of leg.

⇒$3\sqrt{6} = \sqrt{2}x$

Divide both side by $\sqrt{2}$ we have;

$\frac{3\sqrt{6}}{\sqrt{2}} = x$

⇒$\frac{3 \cdot \sqrt{2} \cdot \sqrt{3}}{\sqrt{2}}= x$

Simplify:

$x = 3\sqrt{3}$

therefore, the length of side AB  is, $3\sqrt{3}$ units

Answer 2

Answer:

AB = 3√3

Step-by-step 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