Question 79

A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn, which has an area of 240 sq. m. If the width of the path is 3m and the length of the plot is greater than its breadth by 2m, what is the area of the rectangular plot? (in sq. m.)

Solution

Let length of the plot = $$l$$ m and breadth = $$b$$ m

It is given that, $$l - b = 2$$

Also, Area of lawn = area (AEHD) + area (FBCG) = 240

=> area (ABCD) - area (EFGH) = 240

=> $$(lb) - (3b) = 240$$

=> $$b (b + 2) - 3b = 240$$

=> $$b^2 - b - 240 = 0$$

=> $$(b - 16) (b + 15) = 0$$

=> $$b = 16$$ and $$l = 16 + 2 = 18$$

$$\therefore$$ Area of plot = $$l \times b$$

= $$18 \times 16 = 288 m^3$$

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