Question

The perimeter and area of rectangular play ground are 80m ND 384m square respectively find the length ND breadth of the playground
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Answer 1

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Answer 2

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The perimeter and area of rectangular play ground are 80m ND 384m square respectively find the length ND breadth of the playground

एक आयताकार पार्क का परिमाप 150 मीटर है। यदि इसकी लंबाई 45 मीटर हो तो चौड़ाई कितनी होगी?

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Given : Perimeter of and rectangular playground = 80 m

Area of a rectangular playground = 384 m²

To Find : Length and breadth of the playground.

Solution:

Let the length of the playground be 'L' m and the breadth of the playground be 'B' m.

We know that the perimeter of rectangle,P = 2(length + breadth)

P = 2(L + B)

80 = 2(L + B)

(L + B) = 80/2

L + B = 40

L = 40 - B

Length , L = 40 - B …...(1)

Now, Area, A = Length × Breadth

A = L × B

384 = ( 40 - B) × B

[from eq 1]

384 = 40B - B²

B² - 40B + 384 = 0

Using quadratic formula :

x = [-b ±√(b² - 4ac)]/2a

Here, B = x , a = 1 , b = - 40 , c = 384

B = [-(-40) ±√((-40)² - 4 × 1 × 384)]/2 × 1

B = [40 ±√(1600 - 1536)]/2

B = [40 ±√(64)]/2

B = [40 ± 8]/2

B = 48/2 , 32/2

B = 24 , 16

If Breadth 24 , then length = 40 - x = 40 - 24 = 16

If Breadth 16 , then length = 40 - x = 40 - 16 = 24

Hence, the length and breadth of the playground are 16 m and 24 m.

$\huge\tt\colorbox{yellow}{Explanation}$

A perimeter is either a path that encompasses/surrounds/outlines a shape or its length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden.

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