Question

Mr. Sandeep Kalra is a social worker. He always works for the welfare of his village. In his village there was no school building, Sandeep gave a plot of land for the school building. The length and breadth of the plot are in the ratio $ 10:3. $ He also donated Rs. $ 15,600 $ to fence the plot at Rs. $ 50 $ per m.
I.Find the dimensions of the plot
II.Find the area of the plot.
III.Which value does Mr. Sandeep depict?

Answer 1

Hint: Here we will assume first the length and breadth of the plot. And then will use the formula for the perimeter by using the given cost. Also from the dimensions will find the area of the plot.

Complete step-by-step answer:
Let us assume that the length of the rectangular plot be “l”
And breadth of the rectangular be “b”
Given that the ratio of the length to the breadth is $ 10:3 $
 $ \dfrac{{length}}{{breadth}} = \dfrac{{10}}{3} $
The above equation can be re-written as –
\[ \Rightarrow \dfrac{{breadth}}{{length}} = \dfrac{3}{{10}}\]
Do cross Multiplication –
 $ b = \dfrac{{3l}}{{10}} $ .... (A)
Perimeter of the fence is the sum of all the four sides of the plot.
Perimeter $ = 2(l + b) $
Place value from equation (A)
Perimeter $ = 2(l + \dfrac{{3l}}{{10}}) $
Simplify the above equation –
Perimeter $ = 2\left( {\dfrac{{10l + 3l}}{{10}}} \right) $
Perimeter $ = \dfrac{{26l}}{{10}} $ m
Cost of fencing is $ Rs.{\text{ 50 per m}} $
Cost for fencing $ = \dfrac{{26l}}{{10}} \times 50 $
Given cost is $ 15600 $ place in the above equation –
 $ 15600 = \dfrac{{26l}}{{10}} \times 50 $
Simplify the above equation-
 $ \Rightarrow 15600 \times 10 = 26l \times 50 $
When a term is multiplicative, if it is moved from one side to another then it goes in the denominator.
 $ \Rightarrow l = \dfrac{{15600 \times 10}}{{26 \times 50}} $
Common factors from the numerator and the denominator cancel each other.
 $ \Rightarrow l = 120\;m $ .... (B)
Take equation (A), place the above value in it.
 $ b = \dfrac{{3l}}{{10}} $
 $ \Rightarrow b = 3 \times \dfrac{{120}}{{10}} $
Simplify the above equation –
 $ \Rightarrow b = 36\;m $ ..... ©
So, the correct answer is “$ l = 120\;m $ and $ b = 36\;m $”.

II.Area of the rectangular plot is the product of length and the breadth.
Area $ = l \times b $
Place values from equation (B) and (C)
Area $ = 120 \times 36 $
Area $ = 4320\;{m^2} $
So, the correct answer is “Area $ = 4320\;{m^2} $ ”.

III.Sandeep seems to be a very kind and generous person thinking about the welfare of his village.

Note: Always remember the difference between the area and perimeter. Area is the inside space or the region whereas the perimeter is the outer edge or the surface. Area is measured in square units whereas perimeter in units such as meter, centimetre. Do not forget to write the appropriate unit after the solution.