it is possible to design a reactangular park of perimeter 80m and area

1.	it is possible to design a reactangular park of perimeter 80m and area 400m2? If so, find its length and breadth.
Answer» ANSWER: The length of rectangular park is 20 meter The BREADTH of rectangular park is 20 meter Step-by-step explanation: Given as : The perimeter of rectangular park = 80 meters ∵ perimeter of rectangular park = 2 (length + breadth) LET The length = L m breadth = B m So, perimeter of rectangular park = 2 (L + B) Or, 2 (L + B) = 80 m Or, L + B = $\dfrac{80}{2}$ i.e L + B = 40 m .........1 Again' Area rectangular park = 400 m² Area of rectangular park =A = Length × Breadth So, L × B = 400 m² From eq 1 (40 - B ) × B = 400 Or, 40 B - B² = 400 i.e B² - 40 B + 400 = 0 Or, B² - 20 B - 20 B + 400 = 0 Or, B(B - 20) - 20 (B - 20) = 0 Or, (B - 20 ) (B - 20) = 0 ∴ Breadth = B = 20 m From eq 1 L = 40 m - 20 m i.e Length = 20 m Hence, The length of rectangular park is 20 meter And the breadth of rectangular park is 20 meter . Answer

it is possible to design a reactangular park of perimeter 80m and area 400m2? If so, find its length and breadth.

Answer»

Step-by-step explanation:

Given as :

The perimeter of rectangular park = 80 meters

∵ perimeter of rectangular park = 2 (length + breadth)

LET The length = L m

breadth = B m

So, perimeter of rectangular park = 2 (L + B)

Or, 2 (L + B) = 80 m

Or, L + B = $\dfrac{80}{2}$

i.e L + B = 40 m .........1

Again'

Area rectangular park = 400 m²

Area of rectangular park =A = Length × Breadth

So, L × B = 400 m²

From eq 1

(40 - B ) × B = 400

Or, 40 B - B² = 400

i.e B² - 40 B + 400 = 0

Or, B² - 20 B - 20 B + 400 = 0

Or, B(B - 20) - 20 (B - 20) = 0

Or, (B - 20 ) (B - 20) = 0

∴ Breadth = B = 20 m

From eq 1

L = 40 m - 20 m

i.e Length = 20 m

Hence, The length of rectangular park is 20 meter

And the breadth of rectangular park is 20 meter . Answer