The diagram shows a cube cut in half across one of its diagonal plains. Each edge of the original cube is of length x cm. The diagonal A F has length 20 cm. Calculate the value of x. you must use the algebraic method and show your full working.

Please help me with this question.

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

the answer to the expression is 83

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .