Question

A square lawn has 2m wide path surrounding it. If the area of the path is 136m², dind the area of the lawn.
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Answer 1

Given :-

A square lawn has 2 m wide path surrounding it.

Area of the path = 136m²

To Find :-

The area of the lawn.

Analysis :-

Consider the side length of lawn as a variable.

The area of path is the difference between area of square path and area of lawn.

Then make an equation and get the value of the variable accordingly.

Solution :-

We know that,

• s = Side
• a = Area

Given that,

Area of outer square - Area of inner square = Area of the path

Let us consider the side of the lawn to be 'x'. Then, the side length of path is x + 4

As per the given info,

$\sf (x+4)^{2}-(x)^{2}=136$

$\sf x^{2}+16+8x-x^{2}=136$

$\sf 8x=136-16$

$\sf 8x=120$

Finding the value of x,

$\sf x=\dfrac{120}{8}$

$\sf x=15 \ cm$

Therefore, the length of lawn is 15 cm.

By the formula,

$\underline{\boxed{\sf Area \ of \ square= Side \times Side}}$

Given that,

Side (s) = 15 cm

Substituting their values,

Area = 15²

Area = 225 cm²

Therefore, the area of the lawn is 225 cm².

Answer 2

Answer:

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