Answer

Verified

412.5k+ views

**Hint:**Area of a square of side length a meter is given by \[{{a}^{2}}\] square meters.

Area of a rectangle with length l and breadth b is given by (l x b) square meters. Area of a shape which is a combination of two shapes of area m and n square meters respectively is given by (m + n) square meters.

**Complete step-by-step solution:**

According to the question, the width of the path surrounding the lawn is 2.5 meter. The area of this path is given as 165 square meters.

Consider the side of the lawn to be x. Then the side of the lawn including the path is x+2(2.5) which is simply x+5 meter. Refer the figure given below:

We know that,

(Area of lawn including the path) = (Area of the lawn alone) + (Area of the path)

From this we can write,

(Area of the lawn) = (Area of lawn including path) – (Area of the path)

Then as per the question,

\[{{x}^{2}}={{(x+5)}^{2}}-165\]

\[\Rightarrow {{x}^{2}}=({{x}^{2}}+10x+25)-165\]

\[\Rightarrow {{x}^{2}}={{x}^{2}}+10x+25-165\]

\[\Rightarrow {{x}^{2}}={{x}^{2}}+10x-140\]

\[\Rightarrow {{x}^{2}}-{{x}^{2}}-140=-10x\]

\[\Rightarrow -140=-10x\]

Which means 140=10x

\[\therefore x=\dfrac{140}{10}=14\]

Therefore, the side length of the lawn is 14 meter.

**So, the area of the lawn = \[{{x}^{2}}={{(14)}^{2}}=196\] square meters.**

**Note:**This type of problem can be solved by dividing like: if the width of the path is w meter and its area be y square meters. Let x be the side length of the lawn, then y will be given by y = 2(xw) + 2w(x+2w) which is simply \[y=4xw+4{{w}^{2}}\] from this we get the value of x, side length of the lawn.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE