Question

11) A square and a rectangle are of the same perimeter. The length of the side of the square is 8 cm. If the width of the rectangle is 6 cm, find the length of the rectangle and hence find its area.​

Answer 1

10 cm and 60 cm

Step-by-step explanation:

perimeter of square=4a=4×8=32 cm

perimeter of rectangle=2(l+b)=2(l+6)=2l+12

therefore, 2l+12=32

=> 2l=20

=>l=10

length of rectangle=10 cm

area of rectangle=lb=10×6=60 cm

Answer 2

Answer:

Step-by-step explanation:

Given :

Length of the side of the square 'a' = 8cm

Width of the rectangle 'w' = 6cm

To find :

Length 'l' of the rectangle

Area 'A' of the rectangle

Solution :

It is given that perimeter of the square and rectangle are equal

Perimeter of the square = 4a, where 'a' is one side of the square

Perimeter of the rectangle = 2(l+w), where 'l' is the length and 'w' is the width of the rectangle

Therefore;

4a = 2(l+w) = 2l + 2w

2l  = 4a - 2w

    = 4(8cm) - 2(6cm)

    = 32cm - 12cm

2l  = 20cm

 l  = 10cm

Area of the rectangle;

A = lw

   = 10cm * 6cm

   = 60 $cm^{2}$

Therefore,

The length of the rectangle is 10cm and

Area of the rectangle is 60 $cm^{2}$