Question

style is in a rhombus shape whose diagonals are X + 5 and x minus 8 the the number of tile to floor the number of tile required to float the floor if area of x square - 6 - 20 unit is

Answer 1

Given : A tile is in the shape of rhombus

            Length of diagonals = (x + 5) , (x - 8)

To Find : The number of such tiles required to tile the area of (x² +x - 20) =?

Proof :

Let d1 = (x + 5) units ;  d2 = (x - 8) units

We have,

Area by 1 tile = Area of rhombus

                     = 1/2 × d1 × d2

                     = 1/2 (x + 5)(x - 8) Sq.units

Now,

Area of floor  = x² + x - 20

                      = x² + 5x - 4x - 20

                      =x(x + 5) -4(x + 5)

                      = (x - 4) (x + 5) Sq.units

∴ Number of tiles = Area of floor / area of 1 tile

                             = (x - 4)(x + 5)

                               ______________

                                 1/2 (x + 5)(x - 8)

                              = 2(x - 4)

                                ______

                                  (x - 8)

The number of such tiles required to tile the area of ( x² +x - 20 ) = 2(x - 4) ÷ (x - 8)

                                                                                                             

Answer 2

Thank you for asking this question, here is your answer:

Length of diagonals = ( x + 5 ) , ( x - 8 )

In order to find the area of the tile:

= 1/2 ( x + 5 ) ( x - 8 )

= 1/2 (x² - 8x + 5x - 40 )

= 1/2 ( x² - 3x - 40 )

And the area which needs to be tiled is equal to :

= x² + 5x - 4x - 20  

= x ( x + 5 ) - 4 ( x + 5 )

= ( x - 4 ) ( x + 5 )

In order to find the number of tiles required we will use the following formula:

area to be tiled / area of each tile

(x - 4)(x+5)/1/2(x-8)(x+5)

= 2(x-4)/(x-8)

= 2x - 8/x-8

So the final answer for this question is : 2(x-4)/(x-8)

If there is any confusion please leave a comment below.