Question

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

Answer 1

$\huge\boxed{\fcolorbox{white}{pink}{Answer}}$

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 – l^2 = 400

l^2 –  40l + 400 = 0, which is a quadratic equation.

Comparing the equation with ax^2 + bx + c = 0,

we get

a = 1, b = -40, c = 400

Since, Discriminant = b^2 – 4ac

=>(-40)^2 – 4 × 400

=> 1600 – 1600 = 0

Thus, b^2 – 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, l = 20 m

And breadth of the park, b = 40 – l = 40 – 20 = 20 m.

Answer 2

Given:-

• perimeter of rectangle = 80m

• area of rectangle = 400m^2

To find:-

• Length= ?

• Breadth= ?

Solution:-

Let the length of recatngle be l and breadth be b.

So,

perimeter of rectangle = 2(l+b)

area of rectangle = $l \times b$

So that,

=>2(l+b) = 80m

=> (l+b) = 40m

=> l = (40-b)m

and,

=> $l \times b = 400 {m}^{2}$

$= > (40 - b)b = 400 {m}^{2} \\ = > 40b - {b }^{2} = 400 {m}^{2} \\ = > {b}^{2} - 40b + 400 = 0 \\ = > {b }^{2} - 20b - 20b + 40 0= 0 \\ = > b(b - 20) - 20(b - 20) = 0 \\ = > (b - 20)(b - 20) = 0 \\ = > b = 20m$

l = 40-b

l= 40-20 = 20m

Hence, length = 20m and breadth = 20m

Hope its help uh❤