Question

A tile is in the shape of a rhombus whose diagonals
are (x + 5) units and (x-8) units. The number of
such tiles required to tile on the floor of area (x2 + x - 20) sq. units is

Answer 1

Hey there!

Given,
A tile is in the shape of a rhombus .
Length of diagonals = ( x + 5 ) , ( x - 8 )

Area of the rhombus shaped tile.
= 1/2 ( x + 5 ) ( x - 8 )
= 1/2 (x² - 8x + 5x - 40 )
= 1/2 ( x² - 3x - 40 )

Given area to be tiled = x² + x - 20

Factorising to get the answer easily.

Area to be tiled
= x² + 5x - 4x - 20
= x ( x + 5 ) - 4 ( x + 5 )
= ( x - 4 ) ( x + 5 )

Number of tiles required = $\frac{ \textbf{ Area to be tiled} } { \textbf{Area of each tile }}$

$= \frac{ (x - 4 )( x + 5) }{ 1/2 (x-8)(x+5)} \\ \\ \\ = \frac{2(x-4)}{ (x - 8)} = \frac{ 2x -8}{x-8}$

Final answer : $\frac{2( x - 4 )}{ x - 8 }$

The number of such tiles required to tile the area of ( x² +x - 20 ) is $\frac{2( x - 4 )}{ x - 8 }$

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.