Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m² ? If so, find its length and breadth.

Solution:

Let the breadth of the given rectangle be x m.

Therefore, the length will be 2x m.

Area of a rectangle is given by length × breadth

800 = (x) × (2x) [ Since area is given as 800 m²]

2x² = 800

x² = 800/2

x² = 400

x² - 400 = 0

Discriminant of a quadratic equation ax² + bx + c = 0 is b² - 4ac.

Comparing x² - 400 = 0 with ax² + bx + c = 0 we have,

a = 1, b = 0, c = - 400

b² - 4ac = (0)² - 4(1)(- 400)

= 1600 > 0

As the discriminant is greater than 0, it is possible to have real distinct roots.

Hence, yes, it is possible to design a mango grove.

x² - 400 = 0

x² = 400

x = ± 20

The value of x can’t be a negative value as it represents the breadth of the rectangle.

Therefore, x = 20 m

Length = 2x = 2(20) = 40 m

Breadth = x = 20 m

Thus, it is possible to design a mango grove with length 40 m and breadth 20 m.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 4

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Video Solution:

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m²? If so, find its length and breadth

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.4 Question 3

Summary:

It is possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m² with length and breadth as 40 m and 20 m respectively.

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