✓ Board-verified
Mathematics · 2024 · 4 marks
CBSE 2024 · Region 1 · Set 1 · Q36
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…
A rectangular floor area can be completely tiled with $\displaystyle 200$ square tiles. If the side length of each tile is increased by $\displaystyle 1$ unit, it would take only $\displaystyle 128$ tiles to cover the floor.
(i)
Assuming the original length of each side of a tile be $\displaystyle x$ units, make a quadratic equation from the above information.
(ii)
Write the corresponding quadratic equation in standard form.
(iii)
(a)
Find the value of $\displaystyle x$, the length of side of a tile by factorisation.
OR
(b)
Solve the quadratic equation for $\displaystyle x$, using quadratic formula.
Marking-scheme solution
(i) \(\displaystyle 200 x^{2}=128(x+1)^{2}\)
(ii) \(\displaystyle 25 x^{2}=16 x^{2}+32 x+16\)
\[\Rightarrow 9 x^{2}-32 x-16=0
\]
(iii) (a) \(\displaystyle 9 x^{2}-32 x-16=0\)
\[\begin{aligned}
& \Rightarrow(9 x+4)(x-4)=0 \\
& x \neq \frac{-4}{9} \text { so, } x=4
\end{aligned}
\]
OR
(iii) (b) \(\displaystyle x=\frac{32 \pm \sqrt{1024+576}}{18}=\frac{32 \pm 40}{18}\)
\[x \neq \frac{-4}{9} \text { so, } x=4
\]
All Quadratic Equations questions2024 question paperNCERT solutions: Quadratic EquationsPractice Quadratic Equations →
More from Quadratic Equations
- A quadratic equation whose roots are (2+√3) and (2-√3) is:2023
- Find the value of 'k' for which the quadratic equation (k+1) x^2-2(3 k+1) x+(8 k+1)=0 has real and equal roots. OR A 2-digit number is such that the…2024
- A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway. The total area of the lawn and the walkway is 360…2025
- Find the value(s) of 'k' so that the quadratic equation 4 x^2+kx+1=0 has real and equal roots. OR If ' α ' and ' β ' are the zeroes of the polynomial…2025
- Which of the following equations does not have a real root?2025
- In the picture given below, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk…2022
- In the given figure, a circle is centred at (1, 2). The diameter of the circle is2026
- If the discriminant of the quadratic equation 3 x^2-2 x+c=0 is 16, then the value of c is:2024
CBSE Class 10 Mathematics past-paper question from the 2024 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.