Question

8. A square grass lawn ABCD of area 480 sq m is shown in Fig. 19.65.
A path of uniform width runs all round it, on the outside. If the area of
the path is 145 sq m, find the length of the boundary of the square
field enclosing the lawn.​

Answer 1

Answer:

Don't know the answer .....

Answer 2

100 m is the length of the boundary of the square field enclosing the lawn.​

Given:

• A square grass lawn ABCD of area 480 m²
• A path of uniform width runs all round it,
• Area of Path = 145 m²

To Find:

• The length of the boundary of the square field enclosing the lawn.​

Solution:

• Area = (side)²
• Perimeter = 4 x Side

Step 1:

Area of field Enclosing lawn = Area of Garden +  Area of Path

Step 2:

Substitute Area of Garden = 480 m² and  Area of Path = 145 m²

Area of field Enclosing lawn = 480 +  145

Area of field Enclosing lawn = 625 m²

Step 3:

Assume that side length of enclosing lawn is a m and  find area and equate with 625  and solve for a

a² = 625 m²

a² = 25² m²

a = 25 m

Step 4:

Use Perimeter = 4 x side and substitute side length = 25 m to find length of the boundary of the square field enclosing the lawn.​

4 x 25 = 100 m

Hence, 100 m is the length of the boundary of the square field enclosing the lawn.​