Question

is it possible to design a rectangular Park of perimeter 80m & area 400m2 ? if so, find its length &breadth​

Answer 1

Answer:

this is the answer for this question

Answer 2

Answer:

Yes, it is possible the length and breadth are 20m and 20m respectively.

Step-by-step explanation:

Given :-

Perimeter = 80 m

Area = 400 m²

To find :-

To check whether we can design a rectangular park, if so find length and breadth.

Solution :-

⇛ Perimeter = 80 m

⇛ 2(Length + Breadth) = 80

⇛ Length + Breadth = 80/2

⇛ Length + Breadth = 40

⇛ Let the length be x

⇛ Then, (x + Breadth) = 40

➤ Breadth = 40 - x

⇛ Area = 400 m²

⇛ Length × Breadth = 400 m²

⇛ (x) × (40 - x) = 400 m²

⇛ 40x - x² = 400

⇛ 40x - x² - 400 = 0

➤ x² - 40x + 400 = 0

⇒ -20 - 20 = -40 & 20 × 20 = 400

⇛ x² - 20x - 20x + 400 = 0

⇛ x(x - 20) - 20(x - 20) = 0

⇛ (x - 20) (x - 20) = 0

⇛ x = 20 is the solution

➤ Length (x) = 20 m

➤ Breadth (40 - x) = 40 - 20 = 20 m

Verification :-

✮ Length × Breadth = 400 m²

⇛ 20m × 20m = 400 m²

⇛ 400 m² = 400 m²

➝ L.H.S = R.H.S

✮ 2(Length + Breadth) = 400 m

⇛ 2(20m + 20m) = 80 m

⇛ 2(40)m = 80 m

⇛ 80 m = 80 m

➝ L.H.S = R.H.S