Question

GCSE 3D Pythagoras

The diagram shows a cube cut in half along one of its diagonal planes.
Each edge of the original cube is of length x cm. The diagonal A F has a length of 20 cm.
Calculate the value of x.
You must use an algebraic method and show all your work.

Answer 1

The value of x is equal to (20√3)/3 cm in sure form or 11.5470 cm expressed as a decimal.

Consider the right triangle ABC, AB = x cm and also BC = x cm, the hypotenuse AC can be derived using the Pythagoras rule as follows:

(AC)² = x² + x²

(AC)² = 2x²

AC = √(2x²) {take square root of both sides}

AC = x√2

Also using the Pythagoras rule for the right triangle ACF, we can evaluate the value of x using the derived value of AC = x√2 as follows

x² + (x√2)² = (20)²

x² + 2x² = 400

3x² = 400

x² = 400/3

x = √(400/3) {take square root of both sides}

x = 20/√3

x = 20√3/3 {rationalization}

x = 20√3/3 or 11.5470.

Therefore, the value of x for the cube is derived to be 20√3/3 or 11.5470.