Question

gyes please answer it fast

Answer 1

We know that Area of Rhombus is Given by : 1/2 × d₁ × d₂

where d₁ and d₂ are the lengths of the Diagonals

Given the Lengths of Diagonals of Each Tile :

d₁ = (x + 5)

d₂ = (x - 8)

⇒ Area of Each Tile = $\frac{(x + 5)(x -8)}{2}$

Let 'T' be the Number of such Tiles required to Tile on the Floor of Given Area

⇒ The Product of 'T' Number of Tiles and Area of Each Tile should be Equal to the Total Area of the Floor.

Given the Total Area of the Floor = x² + x - 20

x² + x - 20 can be written as :

⇒ x² + 5x - 4x -20

⇒ x(x + 5) - 4(x + 5)

⇒ Total Area of the Floor = (x + 5)(x - 4)

⇒ $\frac{(T)(x + 5)(x - 8)}{2} = (x + 5)(x - 4)$

⇒ $T = \frac{2(x - 4)}{(x - 8)}$

So, the Number of Tiles Required = $\frac{2(x - 4)}{(x - 8)}$

Option (3) is the Answer