a diagram shows a cube cut in half along one of its diagonal planes each edge of the original cube has a length xcm the diagonal

Question

a diagram shows a cube cut in half along one of its diagonal planes
each edge of the original cube has a length xcm
the diagonal y has a length 20cm

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6 months 2021-07-16T11:18:16+00:00 1 Answers 109 views 0

1. 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