Question

A tile is in the shape of a rhombus whose diagonals are X + 5 units and x minus 8 units the number of such tiles required to tile on the floor of area X square + X - 20 square 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 $\frac{2( x - 4 )}{ x - 8 }$