Half the perimeter of a rectangular garden, whose length is \(4 \) m more than its width is \(36\) m. Find the dimensions of the garden
Half the perimeter of a rectangular garden, whose length is \(4 \) m more than its width is \(36\) m. Find the dimensions of the garden
Solution and Explanation
Let the width of the garden be x and the length be \(y.\)
According to the question,
\(y − x = 4\)………………. (1)
\(y + x = 36\) ……………..(2)
\(y − x = 4 y + x = 36\)
| \(x\) | \(0\) | \(8\) | \(12\) |
| \(y\) | \(4\) | \(12\) | \(16\) |
And \(y + x = 36\)
| \(x\) | \(0\) | \(36\) | \(16\) |
| y | \(36\) | \(0\) | \(20\) |
Hence, the graphic representation is as follows.
From the figure, it can be observed that these lines intersect each other at only points i.e., \((16, 20)\). Therefore, the length and width of the given garden are \(20\) m and\(16\) m respectively.
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Concepts Used:
Graphical Solution of Linear Inequalities In Two Variables
Graphical representation needs the plotting of the x and y in graph paper. Plotting the x and y values of the equation on the coordinate plane. For plotting the graph you will be needed at least 3 sets of points. It is very much important for those points to fall in a straight line. If the points are haphazardly placed, it will indicate some fault in your work.
On the graph paper, draw the x and y-axis. Simply, the x and y-axis are two number lines that are placed perpendicular to each other at the (0,0) point. This point is known to be the origin. Use the aforesaid values for plotting the points. Join all of these points with a straight line.
