Question

What is the length of the diagonal of the square shown below

Answer 1

11√2

Explanation:

Since the diagonal of the square is the hypotenuse of the right triangle whose other sides measure 11 units then we can calculate it by:

`a^(2)=x^(2)+x^(2)\Rightarrow a^(2)=2x^(2)\Rightarrow \sqrt{a^(2)}=\sqrt{2x^(2)}\Rightarrow a=x√(2)`

In addition to this, the diagonal bisects the angle in each corner of the square dividing it into two 45º angles. What help us to explain why the the two triangles formed are isosceles.

Answer 2

The square divided into 2 equal isosceles triangles which are 45 45 90.

The diagonal is the hypotenuse of the triangles

Given leg = 11

Ratio of leg: hypotenuse = x : x√2

So if leg x = 11 the hypotenuse = 11√2

Answer is E. 11√2