Case Study 1:

A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway.

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The total area of the lawn and the walkway is 360 square metres. T

Question

Case Study 1:

A garden designer is planning a rectangular lawn that is to be surrounded by a uniform walkway.

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The total area of the lawn and the walkway is 360 square metres. The width of the walkway is 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:
(i) Formulate the quadratic equation representing the total area of the lawn and the walkway, taking width of walkway $= x$ 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 $₹ 50$ per square metre is $₹ 12{,}000$, calculate the area of the walkway.
(iii) Find the perimeter of the lawn.

Accepted Answer

Step 1: (i) $(12 + 2x)(10 + 2x) = 360$
$4x^2 + 44x - 240 = 0$ or $x^2 + 11x - 60 = 0$
Step 2: (ii)(a) $(x + 15)(x - 4) = 0$
$x = 4$
$	herefore$ Width of the walkway $= 4$ m
Step 3: **OR**
(ii)(b) Area of the walkway $= \frac{12000}{50} = 240$ m$^2$
Step 4: (iii) Perimeter of the lawn $= 2(12 + 10) = 44$ m

Question

Solution