x = (20/√3) cm
Step-by-step explanation:
In this question, we are interested in calculating the length of x.
Now, to do this, we shall be considering two right triangles.
Firstly, let’s take a look at triangle ABC to get the length of AC.
We can see that the length AC is the diagonal of the isosceles triangle ABC(Isosceles as the other two sides have equal length of x cm)
Thus, using Pythagoras’ theorem, the length of AC will be x^2 + x^2 = (AC)^2
(AC)^2 = 2x^2
AC = x √2 cm
Now let’s get X.
To get x, we incorporate a triangle having the length of the diagonal.
The triangle to use here is triangle FAC, with the diagonal being the hypotenuse and the other sides being AC and FC which have the lengths x √2 cm and x cm respectively.
Now, using Pythagoras’ theorem, we can get the length of x
The square of FA equals the square of AC plus the square of FC
Thus, we have
20^2 = (x √2)^2 + x^2
400 = 2x^2 + x^2
3x^2 = 400
x^2 = 400/3
x = √(400/3)
x = (20/√3) cm
