A wire of length 20 cm is bent in different ways to form rectangles. For example Class 9

A wire of length 20 cm is bent in different ways to form rectangles. For example Class 9

Question 1.

A wire of length 20 cm is bent in different ways to form rectangles. For example, we can have a rectangle with length 7 cm and width 3 cm. We can also have one of length 5.5 cm and width 4.5 cm. (Think of a few more ways of forming such rectangles.) Can you write an expression for the area of such rectangles? Class 9

Solution:

Ways of forming rectangles:

i. Length = 9 cm, breadth = 1 cm

ii. Length = 8 cm, breadth = 2 cm

iii. Length = 7.5 cm, breadth = 2.5 cm

Let the length of the rectangle be x.

According to the given condition,

Perimeter of rectangle = 20cm

∴ 2(length + width) = 20cm

∴ 2(x + width) = 20cm

∴ x + width = 10 cm

∴ width = (10 - x) cm

Area of the rectangle = length × width

= x × (10 - x) cm²

= (10x - x²) cm²

∴ The expression for the area of the rectangles is 10x - x².

[Note: There are multiple ways of forming rectangles. Students may write other combinations.]