Question

a rectangular path of width 3m is surrounding the garden whose length is 3m more than its width. if cost of painting the path at rate of 0.5rs/m2 is rs273 then find the area of garden
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Answer 1

Step-by-step explanation:

Given A rectangular path of width 3 m is surrounding the garden whose length is 3 m more than its width. if cost of painting the path at rate of 0.5 rs/m^2 is Rs 273 then find the area of garden

• Now there is a rectangular path whose width is 3m and there is a garden surrounding the 4 sides whose length is 3m more than its width.
• We need to find the area of the garden.
• Let the width of the garden be m meter.
• So we get length of garden will be (m+ 3) m
• According to the question we get
•               (m + 6)(m + 9) – m(m + 3) = 273 / 0.5
•               m^2 + 6m + 9m + 54 – m^2 – 3m = 273 / 0.5
•                    m^2 + 15m + 54 – m^2 – 3m = 546
•                              12 m + 54 = 546
•                                  12 m = 492
•                              m = 41
• So Area of garden = length x breadth
•                                  = (m + 3) x m
•                                 = (41 + 3) x 41
•                                  = 44 x 41
•                                     = 1804 sq m

Reference link will be

https://brainly.in/question/49293847

Answer 2

Answer:

The area of the garden is $1804 m^2$

Step-by-step explanation:

Given, The width of the path = 3 m

           Length of the garden (L) = 3+ width of the garden (W)

          =>  L= 3+W meters ------------> (1)

Now, the total area painted(TAP) is

TAP = (total area including the path) - (only area of the garden)

$[(L+6)(W+6)]-(L*W)= \frac{totalcost}{cost per unit area}$

Now, substituting L= W+3 in the above equation we get

$[(W+9)*(W+6)]-[(W+3)*(W)]=\frac{273}{0.5} = 546$

by simplifying the above equation we get

$12W+54=546$

$W= 41 meters$

Now, substitute the Width(W) in equation (1) we get

Length (L)= 3 + 41 = 44 m

Therefore, the total area of the garden is

$Area = L * W = 44 * 41 = 1804 m^2$

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