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Mathematics · 2025 · 4 marks
CBSE 2025 · Region 3 · Set 1 · Q36
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…
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 $\displaystyle 360$ square metres. The width of the walkway is same on all sides. The dimensions of the lawn itself are $\displaystyle 12$ metres by $\displaystyle 10$ metres. Based on the information given above, answer the following questions:
(i)
Formulate the quadratic equation representing the total area of the lawn and the walkway, taking width of walkway $\displaystyle =\mathrm{x} \mathrm{m}$.
(ii)
(a)
Solve the quadratic equation to find the width of the walkway'x'.
OR
(b)
If the cost of paving the walkway at the rate of ₹ $\displaystyle 50$ per square metre is ₹ $\displaystyle 12,000$, calculate the area of the walkway.
(iii)
Find the perimeter of the lawn.
Marking-scheme solution
(i) \(\displaystyle (12+2 \mathrm{x})(10+2 \mathrm{x})=360\)
\(\displaystyle 4 \mathrm{x}^{2}+44 \mathrm{x}-240=0\) or \(\displaystyle \mathrm{x}^{2}+11 \mathrm{x}-60=0\)
(ii) \(\displaystyle (a)(x+15)(\mathrm{x}-4)=0\)
\(\displaystyle \mathrm{x}=4\)
∴ width of the walkway \(\displaystyle =4 \mathrm{~m}\)
OR
(ii)(b)
Area of the walkway \(\displaystyle =\frac{12000}{50}\)
\(\displaystyle =240 \mathrm{~m}^{2}\)
(iii)
Perimeter of the lawn \(\displaystyle =2(12+10)=44 \mathrm{~m}\)
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CBSE Class 10 Mathematics past-paper question from the 2025 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.