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.

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Assuming th

Question

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.

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Assuming the original length of each side of a tile be $x$ units, answer the following questions:
(i) Write a quadratic equation from the above information.
(ii) Write the corresponding quadratic equation in standard form.
(iii) (a) Find the value of $x$, the length of side of a tile by factorisation.

OR

(b) Solve the quadratic equation for $x$, using quadratic formula.

Accepted Answer

Step 1: (i) $200x^2 = 128(x + 1)^2$
Step 2: (ii) $25x^2 = 16x^2 + 32x + 16$
$\Rightarrow 9x^2 - 32x - 16 = 0$
Step 3: (iii) (a) $9x^2 - 32x - 16 = 0$
$\Rightarrow (9x + 4)(x - 4) = 0$
$x 
eq \frac{-4}{9}$ so, $x = 4$

Question

Solution