A wire of length 20 m is to be folded in the form of a rectangle. How many rectangles can be formed by folding the wire if the sides are posettive integerss in meters?
PLEASE EXPLAIN THIS BRIEFLY AS THIS WEDNES DAY IS MY TEST(14 DECEMBER) AND QUICKLY
Length of the wire = 20 m
Let the length and breadth of the rectangle be l and b respectively.
Perimeter of the rectangle = Length of the wire
∴ 2(l + b) = 20 m
⇒ l + b = 10 m
When l = 9 m, b = 10 – 9 = 1 m
When l = 8 m, b = 10 – 8 = 2 m
When l = 7 m, b = 10 – 7 = 3 m
When l = 6 m, b = 10 – 6 = 4 m
When l = 5 m, b = 10 – 5 = 5 m
When the lengths of the rectangle are taken as 6m, 7m, 8m and 9m, then the breadth of the rectangle are 4m, 3m, 2m and 1m respectively. But, the rectangle of these measurement have been obtained earlier.
Thus, 5 rectangles can be formed by folding the wires, if the sides of the rectangle are positive integers.