Question

A picture is 1.2cm long and 50 cm broad? What is the length of the wooden frame needed for framing the picture? What is the area of the glass required to cover the picture in the frame?

Answer 1

Hint: The wooden frame needed for framing should have the dimension equal to the dimension of the picture so that the picture is fitted in that frame properly and according to the given dimensions we can conclude that the frame will be rectangular.

Complete step-by-step answer:
It is given that the length of the picture is $1.2$ cm and the width of the picture is $50$ cm.
The length of the wooden frame is equal to the perimeter of the picture.
So, we have to find the perimeter of the picture using the formula for the perimeter of the rectangle. The formula is given as:
The perimeter of the picture $ = 2\left( {{\text{length}} + {\text{width}}} \right)$
Put the value of the length as $1.2$ and the width as $50$to find the perimeter of the picture.
The perimeter of the picture $ = 2\left( {1.2 + 50} \right)$
The perimeter of the picture $ = 2\left( {51.2} \right)$
The perimeter of the picture $ = 102.4$ cm
Thus, the perimeter of the rectangular picture is 102.3 cm.
Therefore, the length of the wooden frame is $102.4$ cm, which is needed for framing the picture.

The area of the glass that is required to cover the picture is equal to the area of the rectangular picture, so find the area of the picture using the formula for the area of the rectangle.
The formula for the area of the rectangle is given as:
$
  {\text{Area}} = {\text{length}} \times {\text{width}} \\
  {\text{Area}} = 1.2 \times 50 \\
  {\text{Area}} = 60 \\
 $

Therefore, the area of the glass is $60c{m^2}$ that is required to cover the picture.

Note: Since the glass is used to cover the entire picture, therefore the area of the glass that is needed to cover the picture has the same dimension as the dimension of the picture.
Use the formula for the area of the rectangle and the perimeter of the rectangle because the dimension of the picture concludes that its shape is rectangular.