Question

plz help me with this question
the answer is 225 sq.m​

Answer 1

Question:

A square lawn is surrounded by a 5 metre wide path. if the area of the path is 400 m^2 , find the area of the lawn.

Answer:

The area of lawn is 225 m^2.

Note:

• A square is a parallelogram whose all the sides are equal.

• In a square, both of its diagonal are equal.

• The perimeter of the square is given by;

P = 4•Side

• The diagonal of a square is given by ;

D = √2•Side

• The area of a square is given by ;

A = (Side)^2

• The area of a square is also given by ;

A = (1/2)•(Diagonal)^2

• (A+B)^2 = A^2 + B^2 + 2•A•B

• (A-B)^2 = A^2 + B^2 - 2•A•B

• A^2 - B^2 = (A+B)•(A-B)

Solution:

Let ABCD be the square lawn and PQRS be the lawn along with the path.

Also,

Let the side of the square ABCD be ;

AB = BC = CD = DA = x m.

Then, the side of the square PQRS be ;

PQ = QR = RS = SP = (x+10) m.

Now,

Area of square ABCD = (AB)^2 = x^2

Also,

Area of square PQRS = (PQ)^2 = (x+10)^2

Now,

=> Area of the path = Ar.(PQRS) - Ar.(ABCD)

=> 400 = (x+10)^2 - x^2

=> 400 = (x+10+x)(x+10-x)

=> 400 = (2x+10)•10

=> 400 = 2•(x+5)•10

=> 400 = 20•(x+5)

=> x + 5 = 400/20

=> x + 5 = 20

=> x = 20 - 5

=> x = 15

Thus,

Area of lawn = Area of square ABCD

= (AB)^2

= (x)^2

= (15)^2

= 225

Hence,

The area of the lawn is 225 m^2 .

Answer 2

Question:

A square lawn is surrounded by a path 5m wide. If the area of the path is 400m square find the area of lawn

Given:

A square lawn is surrounded by 5m wide path.

Area of the path = 400m.

To Find:

The area of lawn.

Solution:

Area of path = 400m

Area of ABCD =400m^2

$= \sqrt{400}$

$= 20m$

Length of EFGH = 20m

Length of AB = 20 - 5 = 15m

Area of Square is side × side,

Therefore area of ABCD = 15m × 15m

= 225m^2