DAV Class 8 Maths Chapter 11 Value Based Questions
Understanding Quadrilaterals Value Based Questions
1.
There was a waste land near a locality in the shape of a parallelogram \(ABCD\).
The residents decided to fence the land and convert it into a park with shady trees,
plants and a small herbal garden. The perimeter of the land is \(320\ \text{m}\).
Length \(AB\) of the land is \(100\ \text{m}\). The fencing has to be done only
along sides \(AB, BC\) and \(CD\) of the land. \(AD\) will be used as a gate.
(a) Find the cost of fencing the land at ₹\(26\) per metre.
(b) Do you like the idea of the residents converting waste land into a park? Why?
(c) In what other ways can you make use of waste land?
Solution
(a) Finding the cost of fencing
\[ \begin{aligned} \color{magenta} \text{Opposite sides of } parall & \color{magenta} elogram \text{ are equal} \\[4pt] AB = CD &\implies 100\ \text{m} \\ \text{Let }BC = DA &\implies x \\[8pt] \text{Perimeter of }ABCD &= 320\ \text{m} \\[8pt] AB + BC + CD + DA &= 320 \\[4pt] 100 + x + 100 + x & = 320 \\[4pt] 200 + 2x & = 320 \\[4pt] 2x & = 320 - 200 \\[4pt] 2x & = 120 \\[4pt] x & = \frac{120}{2} \\[4pt] x &= 60\ \text{m} \\[4pt] \therefore BC = DA &\implies 60\ \text{m} \\ \\\text{Length to be fenced} &= AB + BC + CD \\[4pt] &= 100 + 60 + 100 \\[4pt] &= 260\ \text{m} \\ \\\text{Cost per metre} &= \text{₹ }26 \\[4pt] \text{Total cost of fencing} &= 260 \times 26 \\[4pt] &= 6760 \\[4pt] \text{Total cost of fencing} &= \color{green}{\text{₹ }6{,}760} \end{aligned} \](b) Yes. We can get fresh air, enjoy greenery and medicinal plants, and have a clean place for exercise, which is good for our health.
(c) We can also use waste land to build an orphanage, hospital, school or a yoga centre.