Question

Mr. Rana bought a rectangular plot whose length is 4m more than twice the breadth. If the perimeter of the plot is 1128m, find the dimensions of the rectangular plot. Also find the cost of cementing the plot at the rate Rs.1000 per \[100{m^2}\].

Answer 1

Hint:
Here we will first write the relation between the length and the breadth of the plot. Then we will use the formula of the perimeter and equate it to the given value to get the value of the breadth. We will then put the value of breadth of the plot in the relation between length and breadth of the plot to get the value of the length of the plot. Then we will find the value of the area of the plot and find the value of the cost of the cementing of the plot by multiplying the area of plot by the given rate.

Complete step by step solution:
Let \[l\] be the length of the rectangular plot and \[b\] be the breadth of the rectangular plot.
It is given that length is 4m more than thrice the breadth of the rectangular plot. Therefore, using this condition, we get
\[l = 3b + 4\]…………………. \[\left( 1 \right)\]
It is given that the perimeter of the rectangular plot is 1128m. Therefore, we get
Perimeter of the rectangular plot \[ = 2\left( {l + b} \right) = 1128\]
Now we will use the equation \[\left( 1 \right)\] in the above equation and solve it. Therefore, we get
\[ \Rightarrow 2\left( {3b + 4 + b} \right) = 1128\]
Adding the like terms in the bracket, we get
\[ \Rightarrow 2\left( {4b + 4} \right) = 1128\]
Taking 4 common, we get
\[ \Rightarrow 8\left( {b + 1} \right) = 1128\]
Dividing both sides by 8, we get
\[ \Rightarrow b + 1 = \dfrac{{1128}}{8} = 141\]
Subtracting 1 from both the sides, we get
\[ \Rightarrow b = 141 - 1 = 140m\]
Now we will put the value of the breadth in the equation \[\left( 1 \right)\] to get the value of the length of the rectangular plot. Therefore, we get
\[l = 3b + 4 = 3\left( {140} \right) + 4\]
Multiplying the terms, we get
\[ \Rightarrow l = 420 + 4\]
Adding the terms, we get
\[ \Rightarrow l = 424{\rm{m}}\]
Now we will find the area of the rectangular plot.
Substituting \[l = 424\] and \[b = 140\] in the formula of area of rectangle, we get
Area of the rectangular plot \[ = l \times b = 424 \times 140\]
Multiplying the terms, we get
\[ \Rightarrow \] Area of the rectangular plot \[ = 59360{{\rm{m}}^2}\]
It is given the cost of cementing the plot at the rate Rs.1000 per \[100{{\rm{m}}^2}\]. So, multiplying the rate with the area of rectangular plot, we get
Cost of cementing the plot \[ = \dfrac{{59360}}{{100}} \times 1000 = {\rm{Rs}}.593600\]

Hence, the dimensions of the rectangular plot i.e. length is 424m and breadth is 140m and the cost of cementing the plot is Rs. 593600.

Note:
Perimeter is the total length of the outer boundary of a shape in two dimensional. Perimeter is measured in meters. Area is the amount of surface covered by a shape in two dimensional. Surface area is the sum of all the areas of the faces of an object or shape. Area and surface area is measured in square meters. Volume is the amount of space occupied by an object in three-dimensional space. Volume is measured in cubic meters.