Question

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

Answer 1

Given

Perimeter of Rectangular playground is 80m

Area of Rectangular playground is 384m²

To Find

Length and breadth of the Rectangular playground

$\sf\huge \mathbb{\underline{\underline{{Solution}}}}$

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

length = 24m

breadth = 16m

perimeter of playground= 2(24+16)

perimeter of playground= 2×40=80m