# Sooraj’s father wants to construct a rectangular garden

Q:- Sooraj’s father wants to construct a rectangular garden using a brick wall on one side of the garden and wire fencing for the other three sides as shown in the figure. He has 200 metres of fencing wire.

Based on the above information , answer the following question :                    [CBSE   2023]

(i) Let ‘x’  metres denotes the length of the side of the garden perpendicular to the brick wall and ‘y’ metres denote the length of the side parallel to the brick wall. Determine the relation representing the total length of feencing wire and also write A(x), the area of the garden.                     (2)

(ii) Detemine the maximum value of A(x).                       (2)

Solution:- Let ‘x’  metres denotes the length of the side of the garden perpendicular to the brick wall and ‘y’ metres denote the length of the side parallel to the brick wall

Length of fencing wire = 200

x + x + y = 200

⇒ 2x + y = 200

⇒ y = 200 – x

Relation between fencing of wire

y = 200 – x

Area of garden A(x) = x.y

A(x) = x(200 – x) .  .  . (i)

(ii) From equation (i)

A(x) = x(200 – x)

⇒ A(x) = 200x – x²

differentiate with respect to x

.  .  .  (ii)

For maximaa and minima

200 – 2x = 0

⇒ x = 100

Again differentiate with respect to x of eq (ii)

Hence, area of garden is maximaum when x = 100

Now, maximum area

A(x) = x(200 – x)

⇒ A(100) = 100(200 – 100)

⇒ A(100) = 100 × 100 = 10000

Thus the maximum area of garden = 10,000 m²

Q:- A building contractor undertakes a job to construct 4 flats on a plot along with the parking area. Due to strike the probability of many construction workers not being present present for the job is 0.65. The probability that many are not present and still the work get completed on times is 0.35. The probability that work will be completed on time when all workers are present is 0.80.               [CBSE   2023]

Solution:-  See full solution