Question 9 of 11intermediate🔧 ApplyLong Answer3 marks

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2800\text{ m}^2? If so, find its length and breadth.

Correct Answer

Yes, it is possible to design such a rectangular mango grove.

Let the breadth of the rectangular mango grove be xx meters. Then, length = 2x2x meters (since length is twice the breadth).

Area of rectangle = length ×\times breadth

800=2x×x800 = 2x \times x 800=2x2800 = 2x^2 x2=400x^2 = 400 x=±20x = \pm 20

Since breadth cannot be negative, x=20x = 20 meters.

Therefore, breadth = 2020 m and length = 2×20=402 \times 20 = 40 m.

Exercise: EXERCISE 4.3 | Q: 3 | (Page 10)
For More Understanding

Explanation

This question from Exercise 4.3 requires students to form a quadratic equation from a real-life situation. Similar to Example 6 in the textbook where dimensions of a prayer hall were found, students must express length in terms of breadth, form the area equation, solve the resulting quadratic equation, and reject the negative solution since dimensions cannot be negative.

Solution Steps

  1. Step 1: Let breadth = xx m, then length = 2x2x m

  2. Step 2: Form equation using area: 2x×x=8002x \times x = 800

  3. Step 3: Simplify: 2x2=8002x^2 = 800, x2=400x^2 = 400

  4. Step 4: Solve: x=±20x = \pm 20

  5. Step 5: Reject negative value (breadth cannot be negative), x=20x = 20 m

  6. Step 6: Find length = 2×20=402 \times 20 = 40 m

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