Question

Is it possble to design a rectanular park of perimeter 80 and area 400m2? If so fi its lenh and breadth.​

Answer 1

$\huge\underline\mathrm{Question}:-$

Is it possible to design a rectangular park of perimeter 80 and area 400m2? If so find its length and breadth.

$\huge\underline\mathrm{Solution}:-$

Let the length and breadth of the park be L and B.

Perimeter of the rectangular park =

2 (L + B) = 80

So, L + B = 40

Or, B = 40 – L

Area of the rectangular park = L × B = L(40 – L) = 40L – L2 = 400

L2 – 40 L + 400 = 0,

which is a quadratic equation.

Comparing the equation with ax²+ bx + c = 0, we get

a = 1, b = -40, c = 400

Since, Discriminant = b² – 4ac

=>(-40)² – 4 × 400

=> 1600 – 1600 = 0

Thus, b² – 4ac = 0

Therefore, this equation has equal real roots. Hence, the situation is possible.

Root of the equation,

L = –b/2a

L = (40)/2(1) = 40/2 = 20

Therefore, length of rectangular park

↬$\boxed{Length = 20 m}$

And breadth of the park, B = 40 – L = 40 – 20 = 20 m.

↬$\boxed{Breadth = 20m}$

Answer 2

A N S W E R :

• The Length is 20m

• The Breadth is 20m

Given :

• It Possible to design a rectangular park of perimeter 80 and area 400m²

To find :

• Find The Length and Breadth ?

Solution :

• L denote Length
• B denote Breadth

Now, We have,

• Length and Breadth = 400m²
• 2(L + B) = 80

=> L + B = 40 (equation 1)

=> (L + B)² = 1600

=> (L - B)² + 4L, B = 1600

=> (L - B)² = 1600 - 4L, B

=> (L - B)² = 1600 = 1600 = 0

=> L - B = 0 (equation 2)

Now,

• equation (1) + (2)

=> 2L = 40

Hence,

• The Length is 20m

• The Breadth is 20m