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Is it possible to design a rectangular mango Grove whose length is twice is breadth, and the area is 800m square unit . If so, find its length and breadth

Posted by Piyush Nauhwar 5 years, 4 months ago

CBSE > Class 10 > Mathematics

2 answers

? Pranali.A.P ? 5 years, 4 months ago

⇒ Let breadth be x. Then, length will be 2x........ ⇒ Area of rectangular mango grove =800m 2.......... ⇒ x×2x=800........ ⇒ 2x 2... .... =800........ ⇒ x 2 =400................. ∴ x=±20 ⇒ x can not be negative...... ∴ x=20........ ⇒ Breadth of the rectangular mango grove =x=20m....... ⇒ Length of the rectangular mango grove =2x=20×2=40m....

Gaurav Seth 5 years, 4 months ago

Let the breadth of the rectangular mango grove be x m
So, length = ‘2’ m
According to question,
Area = 800
⇒ 2x(x) = 800
⇒ 2x² = 800
⇒ x² = 400
⇒ x² – 400 = 0
⇒ x² + 0x – 400 = 0
Here, a = 1, b = 0, c = – 400
D = b² – 4ac
= 0 – 4(1) (–400)
= 1600
So, the given quadratic equation has real roots (∵ D > 0) and hence it is possible to design rectangular mango grove.
Now, solving the quadratic equation x² + 0x – 400 = 0, by quadratic formula, we get,

∵    is not possible
So,
Hence, breadth of the rectangular mango grove is 20 m and length is 40 m.

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