Question

Q1.the perimeter and area of rectangular playground are 80m and 384square metres respectively. Find the length and breadth of playground. ​

Answer 1

Explanation:

Given

Perimeter of Rectangular playground is 80m

Area of Rectangular playground is 384m²

To Find

Length and breadth of the Rectangular playground

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Since,the playground is in rectangular form so,we can apply formula of Rectangle of area and perimeter.

Perimeter of playground= 2(l+b)

Where ,l is the length and b is the breadth

➙2(l+b)=80

➙l+b= 40

l= 40-b-----(1)

Area of Rectangular playground =length × breadth

➙l×b=384

From equation 1 substitute the value of l in this

➙(40-b)b= 384

➙40b-b²-384

➙-b²+40b-384=0

➙b²-40b+384=0

➙b²-24b+16b+384=0

➙b(b-24)-16(b-24)

➙(b-16)(b-24)=0

b= 16 or 24

Put b in Equation 1

When b = 16

➙l= 40-16= 24

when b = 24

➙l= 40-24= 16

We get two values of both length and breadth

length = 24m or 16m

Breadth = 16m or 24m

Check :

length = 24m

breadth = 16m

perimeter of playground= 2(24+16)

perimeter of playground= 2×40=80m

Answer 2

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★let say Length = x m

Breadth = Bm

2(length + breadth ) Perimeter

=> 2(x + B) = 80

=> x + B = 40

=> B = 40 - x m

Area = Length * Breadth

=> 384 = x ( 40 - x)

=> 384 = 40x - x²

=> x² - 40x + 384 = 0

=> x² - 24x - 16x + 384 = 0

=>(x-24)(x - 16) = 0

=> x = 24 or 16

=> 40 x = 16 or 24

length and breadth are 16 & 24 m.

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