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 $cm^{2}$.

Step-by-step 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 × $\frac{10}{100}$ )

                              = 8.8

                           b = 5 + ( 5 × $\frac{10}{100}$ )

                              = 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.