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The length of a plot is four times its breath. A playground measuring 400 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?
- a)20
- b)30
- c)60
- d)40
- e)80
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
The length of a plot is four times its breath. A playground measuring ...
Area of the plot = (4 x 400) m²
= 1600 m²
Breadth = y meter
Length = 4y meter
Now area = 4y x y = 1600 m²
⇒ y² = 400 m²
⇒ y = 20 m
∴ Length of plot = 4y =80 m
= 1600 m²
Breadth = y meter
Length = 4y meter
Now area = 4y x y = 1600 m²
⇒ y² = 400 m²
⇒ y = 20 m
∴ Length of plot = 4y =80 m
Most Upvoted Answer
The length of a plot is four times its breath. A playground measuring ...
To solve this problem, we need to use the given information to find the length of the plot. Let's break down the information step by step:
1. The length of a plot is four times its breadth: Let's assume the breadth of the plot is 'x'. According to the given information, the length of the plot would be 4x.
2. A playground occupies one fourth of the total area of the plot: The area of the playground is given as 400 square meters. Since the playground occupies one fourth of the total area of the plot, we can calculate the total area of the plot by multiplying the area of the playground by 4. So, the total area of the plot would be 400 * 4 = 1600 square meters.
3. Now, we can use the total area of the plot to find the length. The formula to calculate the area of a rectangle is length * breadth. We know that the area of the plot is 1600 square meters and the length is 4x. Substituting these values into the formula, we get:
4x * x = 1600
4. Simplifying the equation, we have:
4x^2 = 1600
5. Dividing both sides of the equation by 4, we get:
x^2 = 400
6. Taking the square root of both sides, we get:
x = √400
7. Simplifying the square root, we have:
x = 20
8. Since the length of the plot is four times its breadth, we have:
Length = 4x = 4 * 20 = 80 meters
Therefore, the length of the plot is 80 meters. The correct answer is option E.
1. The length of a plot is four times its breadth: Let's assume the breadth of the plot is 'x'. According to the given information, the length of the plot would be 4x.
2. A playground occupies one fourth of the total area of the plot: The area of the playground is given as 400 square meters. Since the playground occupies one fourth of the total area of the plot, we can calculate the total area of the plot by multiplying the area of the playground by 4. So, the total area of the plot would be 400 * 4 = 1600 square meters.
3. Now, we can use the total area of the plot to find the length. The formula to calculate the area of a rectangle is length * breadth. We know that the area of the plot is 1600 square meters and the length is 4x. Substituting these values into the formula, we get:
4x * x = 1600
4. Simplifying the equation, we have:
4x^2 = 1600
5. Dividing both sides of the equation by 4, we get:
x^2 = 400
6. Taking the square root of both sides, we get:
x = √400
7. Simplifying the square root, we have:
x = 20
8. Since the length of the plot is four times its breadth, we have:
Length = 4x = 4 * 20 = 80 meters
Therefore, the length of the plot is 80 meters. The correct answer is option E.
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The length of a plot is four times its breath. A playground measuring 400 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?a)20b)30c)60d)40e)80Correct answer is option 'E'. Can you explain this answer?
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