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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 - CBSE Class 10 - Mathematics

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Question

 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 1

Let the breadth of mango grove be l.

Length of mango grove will be 2l.

Area of mango grove = (2l) (l)= 2l2

2l2 = 800

l2 = 800/2 = 400

l2 - 400 =0

Comparing this equation with al2 + bl + c = 0, we get

a = 1, b = 0, c = 400

Discriminant = b2 - 4ac = (0)2 - 4 × (1) × ( - 400) = 1600

Here, b2 - 4ac > 0

Therefore, the equation will have real roots. And hence, the desired rectangular mango grove can be designed.

l = ±20

However, length cannot be negative.

Therefore, breadth of mango grove = 20 m

Length of mango grove = 2 × 20 = 40 m

Solution 2

Let the breadth of the rectangular mango grove be meter and the length 2x meters. Then

Area of the rectangle

length x breadth = 800

x(2x) = 800

2x2 = 800

x2 = 400

`x=sqrt400=+-20`

Sides of the rectangular hall never be negative

Therefore, length

= 2x = 2(20) = 40

Yes, it is possible.

Hence, breadth of the hall be 20 meters and length be 40 meters.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 4: Quadratic Equations
Ex.4.40 | Q: 3 | Page no. 91
 NCERT Solution for Mathematics Textbook for Class 10 (2018 to Current)
Chapter 4: Quadratic Equations
Ex.4.40 | Q: 3 | Page no. 91
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 Concept: Nature of Roots.
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