Question

a floor is paved with 75 square tiles of a size . if rectangular tiles of a length 4 centimetre bigger and breadth 1 cm less than that of the score where tiles were used only 64 tiles are needed find the length of the square tile.​

Answer 1

$1.Let \: a \: side \: of \: each \: square \: tile = x\:cm$

$Area \: of \: each \: tile = x^{2} \:cm^{2}$

$Number \: of \: tiles \: paved \: the \:floor =75$

$\blue { Area \:of \:75 \:tiles}$

$\blue { = 75x^{2} \:cm^{2} }\: --(1)$

/* According to the problem given */

Dimensions of a rectangular tile:

$Length (l) = ( x+4) \:cm$

$Breadth (b) = ( x - 1 ) \:cm$

$Area \: of \: each \:tile = (x+4)(x-1) \:cm^{2}$

$\orange {Area \: of \: 64 \: tiles }$

$= 64(x+4)(x-1)$

$= 64( x^{2} - x + 4x - 4 )$

$= 64( x^{2} + 3x - 4 )$

$\orange {= (64x^{2} + 192x - 256) \:cm^{2}}\: ---(2)$

/* Form equation (1) and equation (2) */

$75x^{2} = 64x^{2} + 192x - 256$

$\implies 75x^{2} - 64x^{2} - 192x + 256 = 0$

$\implies 11x^{2} - 192x + 256 = 0$

/* Splitting the middle term,we get */

$\implies 11x^{2} - 176x - 16x + 256 = 0$

$\implies 11x(x - 16) - 16( x - 16 ) = 0$

$\implies (x-16)(11x-16) = 0$

$\implies x-16 = 0 \: Or \: 11x-16 = 0$

$\implies x = 16 \: Or \: 11x= 16$

$\implies x = 16 \: Or \: x= \frac{16}{11}$

Therefore.,

$\red{ Length \:of \: the \: square \:tile }$

$\green { = 16 \:cm \: Or \: \frac{16}{11}\:cm}$

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