Question

the area of rhombus whose diagonals are 3 unit and 4 unit is​

Answer 1

Answer:

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

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 }}

Area of each tile

Area to be tiled

\begin{gathered} = \frac{ (x - 4 )( x + 5) }{ 1/2 (x-8)(x+5)} \\ \\ \\ = \frac{2(x-4)}{ (x - 8)} < br / > = \frac{ 2x -8}{x-8} \end{gathered}

=

1/2(x−8)(x+5)

(x−4)(x+5)

=

(x−8)

2(x−4)

<br/>=

x−8

2x−8

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

x−8

2(x−4)