Solve the following:
1. The floor of a room has length $9.72 m$ and breadth $7.68 m$ .This floor is to be covered by square tiles of largest size. Find the length of the side of each of such tiles.
2. A trader jethalal ghada bought (x-2) T.V. sets for Rs $2 x^{4} + 5 x^{3} - 7 x^{2} - 15 x - 14.$ find the price of T.V. set.

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Solution

(1) Length of floor $= 9.72 m = 972 c m$
Breadth of floor $= 7.68 m = 768 c m$
To find the largest possible size of square till we need to find the HCF of $972$ and $768$ .
$972 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3$
$768 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
HCF $= 2 \times 2 \times 3 = 12 c m$
SIze of tile $= 12 c m \times 12 c m$
Area $= 12 \times 12 = 144 {c m}^{2}$

(2) Price of each T.V set $= \frac{{2 x}^{2} + {5 x}^{3} - {7 x}^{2} - 15 x - 14}{x - 2}$

Cost of TV set $= R s . {2 x}^{3} + {9 x}^{2} + 11 x + 7$

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