Question

Find the value of the variable if the answer is not an integer leave it in its simplest form

Answer 1

Let us begin by redrawing the diagram for clarity:

The triangle is a right-angled triangle with the following sides:

Hypothenuse side = x

Adjacent side = 12

Opposite side = 12

To solve for x, we have to apply Pythagoras theorem which is defined as:

$Hyp^2\text{ = Opp}^2\text{ + Adj}^2$

Substituting and solving for x:

$\begin{gathered} x^2\text{ = 12}^2\text{ + 12}^2 \\ x^2\text{ = 288} \\ x\text{ = }\sqrt{288} \\ x\text{ = }\sqrt{144\text{ }\times2} \\ =\text{ 12}\sqrt{2} \end{gathered}$

Hence, the correct option is Option B