Question

A square lawn is surrounded by a path 2.5m wide.If the area o the path is 175m square,find the area of lawn

Answer 1

Correct question:-

• A square lawn is surrounded by a path 2.5m wide.If the area of the path is 165m square, find the area of lawn.

$\huge\frak{Answer :}$

Given:-

• A square lawn is surrounded by a path 2.5m wide and the area of the path is 165m²

To find:-

• Area of the lawn

Solution:-

Let side of lawn be x,

Side of the lawn including path = x + 2 (2.5) = x+5

As we know that,

• Area of square = side²

So, area of lawn = (Area of the lawn including the path) - (Area of the path)

⇢ x ² = (x + 5)² - 165

⇢ x² = x² + 10x + 25 - 165

⇢ x² = x² + 10x - 140

⇢ - 10x = - 140

⇢ x = - 140/ - 10

⇢ x = 14

• Side of lawn = 14m

• Area = (14)² = 196m²

Hence, the area of the lawn is 196m².

Answer 2

Question:-

A square lawn is surrounded by a path 2.5m wide.If the area of the path is 165 m square, find the area of lawn.

Answer :-

Area of the lawn is 196m²

Given:-

• A square lawn is surrounded by a path 2.5m wide

• Area of the path = 165m²

Have to find:-

What is the area of the lawn ?

Calculations :-

Considering the side of lawn = " x " metre.

Now, According to the Question :-

Given Side of the lawn + measurement of path

= x + 2 × 2.5

= ( x + 5 ). ...... (1)

As we know that,

Using formula of area of square .

Area of square = side²

Firstly find out the side ,

As we know Area of lawn = ( Total area of lawn + the path) - ( Area of the path )

↠ x ² = (x + 5)² - 165

↠ x² = x² + 10x + 25 - 165

↠ x² = x² + 10x - 140

$\longmapsto\tt{ - 10x = - 140}$

$\longmapsto\tt{\cancel\dfrac{- 140}{- 10}=x}$

$\large{\boxed{\bold{x\:=\: 14\:m}}}$

↠ Therefore we got the Side of lawn ↠ 14m

So , we can easily find out the area by using the formula :-

Area = ( Side ) ²

↠ (14)²

↠ 196m²

$\therefore\underline{\boxed{\textsf{A = {\textbf{196m Sq.}}}}} \qquad\qquad \bigg\lgroup\bold{Area \ of \ the \ lawn} \bigg\rgroup$

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .

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