A rectangle has a perimeter of 66 ft. and an area of 216 ft. square.

Question

find the dimensions?

Answer 1

Let l is length of rectangle and b is breadth of rectangle.

Rectangle perimeter = 66ft

Formula for rectangle perimeter = 2 (l + b)

2(l + b) = 66

l + b = 66/2

l + b = 33

l = 33 - b ---> (1)

Area of the rectangle  = 216 ft²

Formula for rectangle area = lb

lb = 216 ---> (2)

From equation (1), substitute the value of l in equation (2).

(33 - b)b = 216

33b - b² = 216

b² - 33b + 216 = 0

Solve the above equation for b.

b² - 24b - 9b + 216 = 0

b(b - 24) - 9(b - 24) = 0

(b - 24)(b - 9) = 0

b = 9 and 24

Substitute b = 9 in l = 33 - b

l = 24 .

Substitute b = 24 in l = 33 - 24

l = 9 .

The dimensions of rectangle = 24ft and 9ft.

In rectangle length is always greater than breadth.

l = 24ft and b = 9ft.