Question

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

Answer 1

Answer:

The answer is 225 m sq.

Step-by-step explanation:

so we know that area of outer lawn (ABCD) is given 400 m sq.

now ,

The area of square -

side² = 400 m ²

side = √400 m

side = 20 m

now in sq. EFGH -

20 - 5 = 15 ( side of inner square)  . ..

area of outer square =

side ² = 15 ²

= 225 m²

Answer 2

Given:

A square lawn is surrounded by a 5m wide path.

Area of path is 400m²

To Find:

Area of the lawn

Solution:

Let us assume the side of square lawn be = x

Now ATQ

A square lawn is surrounded by a 5m wide path.

Side of lawn including the path

= 5 + x + 5 = (x + 10)m

Now

Area of lawn = Area of lawn(with path) - Area of path

x² = (x+10)² - 400

x² = x² + 20x +100 -400

20x = 300

x = 15m

Area of lawn = x² = (15)² = 225m²

Hence, area of lawn is 225m².