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Maths (Standard) - 2024 (30-1-1) Set-1 — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsMaths (Standard) - 2024 (30-1-1) Set-14 Marks
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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$(i)$ 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.
$(iii) (a)$ 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.
✓

Answer

$(i)\ 200 x^2=128(x+1)^2$
$(ii)\ 25 x^2=16 x^2+32 x+16$
$\Rightarrow 9 x^2-32 x-16=0$
$(iii)\ (a)\ 9 x^2-32 x-16=0$
$\Rightarrow(9 x+4)(x-4)=0$
$x \neq \frac{-4}{9}$
so, $x=4$
OR
$(iii)\ (b)\  x =\frac{32 \pm \sqrt{1024+576}}{18}=\frac{32 \pm 40}{18}$
$x \neq \frac{-4}{9}$
so, $x=4$

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