Question

Mr Chopra wants to put a wooden border around a painting. If the length of the painting is $40{\rm{ cm}}$ and its breadth is $25{\rm{ cm}}$, what will be the cost of putting the border at Rs.$40$ per m ?

Answer 1

Hint:
We know that the wooden border around the painting is in a rectangular shape and also its length and breadth are given. We have to calculate the cost of putting the border around the painting. Since we have to cover the painting around its corners, which means that the length of the total wooden border around the painting would be equal to the perimeter of the rectangle. We know the formula for the perimeter of the rectangle,
\[{\rm{Perimeter}} = \left( {{\rm{Length}} + {\rm{Breadth}}} \right)\]
Given:
The length of the painting $l = 40{\rm{ cm}}$
The breadth of the painting $b = 25{\rm{ cm}}$
And, the rate of putting the border $
 = {\rm{ Rs}}{\rm{. }}40{\rm{ per\ \ m}}\\
{\rm{ = Rs}}{\rm{. }}\dfrac{{40}}{{100}}{\rm{ per\ \ cm}}
$

Complete step by step solutions :
So, the perimeter of the painting using the formula for the perimeter of the rectangle is given by –
Perimeter \[P = \;2\left( {l + b} \right)\]
Substituting the values of $l$ and $b$ in the formula we get,
$
P = 2\left( {40 + 25} \right)\\
 = 2 \times 65\\
 = 130{\rm{ cm}}
$
So, the cost of putting the border $ = $ Perimeter of the painting $ \times $ the rate of putting the border
Substituting the values, we get,
The cost of putting the border $ = 130{\rm{ cm}} \times \dfrac{{40}}{{100}}{\rm{ per\ \ cm}}$
Solving this we get,
The cost of putting the border $ = {\rm{Rs}}{\rm{. }}52$

Therefore, the cost of putting the border is ${\rm{Rs}}{\rm{. }}52$.

Note:
It should be noted that while solving this question the units of the distance given should be the same. For example, the rate of the border was given in $cm$ but the length and breadth were given in the $m$, so either change $cm$ into $m$ or $m$ into $cm$ using the conversion formula.
The conversion formula used is – $1{\rm{ m = 100 cm}}$