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Mathematics · 2022 · 4 marks
CBSE 2022 · Region 3 · Set 1 · Q13
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…
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 around the pool of width x m. The outside edges of the sidewalk measure $\displaystyle 7$ m and $\displaystyle 12$ m. The area of the pool is $\displaystyle 36$ sq. m.
(a)
Based on the information given above, form a quadratic equation in terms of x.
(b)
Find the width of the sidewalk around the pool.
Marking-scheme solution
(a)
Sides of pool are \(\displaystyle 7-2 x\) and \(\displaystyle 12-2 x\)
\[\text { Area }=36 \text { sq. m }
\]
\[\begin{aligned}
& \Rightarrow(7-2 x)(12-2 x)=36 \\
& \Rightarrow 4 x^{2}-38 x+48=0
\end{aligned}
\]
(b)
\[\begin{aligned}
& \Rightarrow 2 x^{2}-19 x+24=0 \\
& \Rightarrow(x-8)(2 x-3)=0 \\
& x \neq 8 m \therefore x=\frac{3}{2} m
\end{aligned}
\]
∴ width of sidewalk around the pool is \(\displaystyle \frac{3}{2} \mathrm{~m}\)
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CBSE Class 10 Mathematics past-paper question from the 2022 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.