Question

A tile is in the shape of the rhombus whose diagonals are (x+5) and (x-8) units. The no of tiles required to tile on the floor of area (x^2+x-20) sq. units is

Answer 1

Answer: $\text{Number of tiles }=\frac{2(x-4)}{x-8}$

Explanation:

Since we have given that

Diagonals of rhombus are given by

$(x+5)\text{ and }(x-8)$

And we have the area of floor is given by

$x^2+x-20\text{ sq. units}$

Now, we need to find the number of tiles so we use the formula, which is given by

$\text{ Number of tiles}=\frac{\text{ Area of floor}}{\text{ Area of 1 tile}}$

For this we need to calculate the area of tile which is in the form of rhombus ,so,

$\text{ Area of rhombus}\\\\=\frac{1}{2}\times d_1\times d_2\\\\=\frac{1}{2}\times (x+5)(x-8)$

And we simplify the equation of area of floor

$x^2+x-20\\\\=x^2+5x-4x+20\\\\=x(x+5)-4(x+5)\\\\=(x+5)(x-4)$

So,

$\text{Number of tiles }\\\\=\frac{(x+5)(x-4)}{\frac{1}{2}(x+5)(x-8)}\\\\=\frac{2(x-4)}{x-8}$

Hence,

$\text{Number of tiles }=\frac{2(x-4)}{x-8}$

Answer 2

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