CBSE Class 10 Maths (Standard) 2025 · Paper 30/3/1 · Question 36

Quadratic Equations 4 marks Medium

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

square metres. The width of the walkway is the same on all sides. The dimensions of the lawn itself are

12

metres by

10

metres. Based on the information given above, answer the following questions:

Schematic: rectangular lawn (12 m by 10 m) with uniform walkway of width x around it.

(i)Formulate the quadratic equation representing the total area of the lawn and the walkway, taking width of walkway $= x$ m.[1]
(ii)(a)Solve the quadratic equation to find the width of the walkway ' $x$ '.[2]
(ii)(b) (OR)If the cost of paving the walkway at the rate of Rs. $50$ per square metre is Rs. $12, 000$ , calculate the area of the walkway.[2]
(iii)Find the perimeter of the lawn.[1]

Answer

(i)

(12 + 2 x) (10 + 2 x) = 360

, that is,

x^{2} + 11 x - 60 = 0

; (ii)(a) The width of the walkway is

x = 4

m; (ii)(b) The area of the walkway is

240 m^{2}

; (iii) The perimeter of the lawn is

44

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