Question

What is the value of x?
O 1/3√2 units
O 1/2√3 units
O 2√3 units
O 3√2 units

Answer 1

Option 4

Explanation:

There are two main ways to find x in this question.
The first one is using similar triangles, like the title of the question states.
We can see that the 2 right angled triangles are similar (this can be proven using angles) so we can set up an equation as the ratio of corresponding sides are equal:

x/3 = 6/x

x² = 18

x = √18 = 3√2 units

Alternatively, we can see that the blue line is a perpendicular bisector of the larger triangle, so the large triangle is also isosceles. Hence using Pythagoras,

x² + x² = 36

x² = 18

x = 3√2 units