Question

A tile is in the shape of a rhombus whose diagonal are (x+5) and (x-8) units. The number of such tiles required to tile on the floor of area (x^2+x-20) square units is

Answer 1

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.