The length of the plot of land is 4 times its breadth.A playground measuring 1200 sq. M. Occupies one-third of the total area of the plot.What is the length of the plot in metres?
Answers
Given data : The length of the plot of land is 4 times its breadth. A playground measuring 1200 m². Occupies ⅓ of the total area of the plot.
To find : what is the length of plot in meters ?
Solution : a/c to question;
- length = 4 breadth
- l = 4 b ----{1}
- area of playground = 1200 m²
Playground occupies ⅓ of the total plot.
Hence, area of plot = 1200 * 3 = 3600 m²
Now, assume that the shape of the plot be rectangular, We use formula of area of rectangle,
⟹ Area of plot = length * breadth ----{2}
⟹ 3600 = 4b * b
⟹ 4b² = 3600
⟹ b² = 3600/4
⟹ b² = 900
⟹ b = √900
⟹ b = 30 m
put value of in eq. {1}
⟹ l = 4 * b
⟹ l = 4 * 30
⟹ l = 120 m
Answer : Hence, the length of the plot is 120 m.
{verification : now put value of l and b in eq. {2}
⟹ Area of plot = length * breadth
⟹ Area of plot = 120 * 30
⟹ Area of plot = 3600 m²
Hence it verified.}
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