Question

Andy’s friend Sandy also got his land restructured. In his case, the land was rectangular before. Keeping the same base and same parallels, LandGrabbers restructured it into a parallelogram-shaped land as shown in the figure. Sandy spent Rs. 400 on fencing and Rs. 500 on ploughing earlier. If AE is twice of AD, find the extra amount he has to spent now on fencing and ploughing respectively in terms of ‘x’ and ‘y’.

Answer 1

Perimeter before restructuring the land = 2 (AB + AD) = 2 (x + y) units

Money spent on fencing before = Rs. 400

Charge for fencing = $\frac{Rs.400}{2(x+y)}=\frac{Rs.200}{(x+y)}$

So, the charge is $\frac{Rs.200}{(x+y)}$ per meter.

New perimeter of the parallelogram shaped land = 2 (AB + AE) = 2 (x + 2y) [Since AE = 2AD]

Difference in cost of fencing now = $\frac{Rs.200}{(x+y)}$ $\times$ Difference in perimeters

$=\frac{Rs.200}{(x+y)}\times \left[2\right(x+2y)-2(x+y\left)\right]=\frac{Rs.200}{(x+y)}\times 2y$

Similarly, difference in the cost of ploughing

= (Cost of ploughing per square units) $\times$ Difference in areas

= Rs. 0 (Since difference in areas of two lands is zero reason being parallelograms having the same base and between the same parallels have equal area)