Question

the perimeter of the rectangular field is 82 cm. Taking x as it's breadth find the length is term of x find its dimensions if it's area is 400 square​

Answer 1

Given: Perimeter as 82 cm, area as 400 cm²

To find: find the length is term of x, find its dimensions

Solution:

• Now we have given that the perimeter of the rectangular field is 82 cm and area of the rectangular field is 400 cm².

• We have asked to take breadth as x.

• Now perimeter of rectangle is 2l + 2x

• Here l is length and breadth is x.

• So:

                Perimeter = 2l + 2x

                82 = 2(l + x)

                41 = l + x

                l = 41 - x

• So length in terms of x is 41 - x.

• Now area = l × x

                400 = (41 - x)(x)

                400 = 41x - x²

                x² - 41x + 400 = 0

                x = 41 ± √41² - 4(1)(400) / 2(1)

                x = 41 ± √1681 - 1600) / 2

                x = 41 ± √(81) / 2

                x = 41 ± 9 / 2

                x = 50/2 , 32/2

                x = 25 , 16

Answer:

              So, if breadth is 16, then length will be 25.