Question

Find sides of rectangle whose perimeter is 100m and area 600cm

Answer 1

Let the length and breadth of the rectangle be x and y respectively,

According to the question,

Area of Rectangle = 600 cm²

==> Length × Breadth = 600

==> x × y = 600

==> x = 600/y ...(1)

Also,

Perimeter of Rectangle = 100 cm

==> 2(x + y) = 100

==> x + y = 50 ...(2)

==> 600 / y + y = 50

==> 600 + y² = 50y

==> y² - 50y + 600 = 0

==> y² + 60y - 10y + 600 = 0

==> y( y + 60) - 10 ( y + 60) = 0

==> (y + 60)(y - 10) = 0

y = -60 or y = 10

Since, length can't be negative so -60 is neglected.

y = 10

Put value of y in (2)

==> x + y = 50

==> x = 50 - y

==> x = 50 - 10

==> x = 40

Hence, The length of the rectangle is 40 cm and breadth of the rectangle is 10 cm.