Question

a rectangle field has an anrea of 40cm^2. if one side of the field is 3m longer than the other side, find the new area of the field where the length of each side is increased by 10%​

Answer 1

The area of the field where the length of each side is increased by 10% is 48.4
`cm^(2)`.

Explanation:

The given is,

A rectangle field has an area of 40
`cm^(2)`

If one side of the field is 3 cm longer than the other side

The length of new area in each side is increased by 10%

Step:1

Let,

`b` - One side of rectangle

`l` - Other side of rectangle

From given.

`l` -
`b` +3

Formula for area of rectangle,

`Area, a = lb`

40 = ( b+3) × b

40 =
`b^(2)` + 3b

Solving the above the equation,

b = 5 cm

l = 8 cm

Step:2

If the area of rectangle increased by 10%,

l = 8 + ( 8 ×
`(10)/(100)` )

= 8.8

b = 5 + ( 5 ×
`(10)/(100)` )

= 5.5

Area of rectangle is,

a = ( 8.8 × 5.5 )

= 48.4 square centimeters

Result:

The area of the field where the length of each side is increased by 10% is 48.4
`cm^(2)`, if a rectangle field has an area of 40 square centimeters and one side of the field is 3 cm longer than the other side.