(Q) A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor.
(i) Assuming the original length of each side of a tile be x units, make a quadratic equation from the above information.

(ii) Write the corresponding quadratic equation in standard form.

(iii) Find the value of x, the length of side of a tile by factorisation.

Ans:  Let’s consider the side of a tile is x units.

Therefore the area of 1 tile = sq. units

Hence, area of 200 tiles = 200 sq. units

Next, The tile size is increased by 1 unit, the new side f tile = units

Hence, area of a new tile = sq. units

(i) Making the Quadratic equation:

By given condition, area of floor is covered by 200 old tiles or 128 new tiles,

Therefore, 200 = 128

(ii) Quadratic equation in standard form:

A quadratic equations standard form is

we need to bring the above equation in above standard form.

By solving the equation, we get:

(iii) Find the value tile’s side:

Let’s solve this quadratic equation:

Here,

Here, we reject , because the value of a tile’s side can not be negative number.

Hence x = 4

Therefore the side of the tile is 4 units

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