The triangular based pyramid ABCD is shown. The base ABC is right angled triangle and the pyramid has a volume of 72cm3. D is directly above A. AB=AC. AD= 2 * AB. The length AB is labelled X. Calculate x

AB = AC = 6 cm

AD = 6*2 = 12 cm

Step-by-step explanation:

Solution:-

- A small sketch of a right angle triangular base pyramid could help use visualize the right angle triangle base ( A B C )

Where Length,

                     AB = AC = x

                     AD = 2*AB = 2x

Where, The point D directly above A.

- The volum ( V ) of a pyramid is given by:

                    V = [ Base Area * h ] / 3

- Where,    Base Area : The area of triangle ABC

                 h : The total height of the pyramid, AD

- The base area of the triangular base  ( A B C ) is given by:

                   Base area  = 0.5*AB*AC

                                      = 0.5*x*x

                                      = 0.5x^2

- The height of the pyramid, AD = 2*AB = 2*x

- Compute the value of x, for the given volume V = 72 cm^3:

                    3*V = 0.5x^2* 2x

                    3*72 = x^3

                    216 = x^3

                    x = 6 cm

452,489 to the nearest thousand is 452,000