the perimeter and area of rectangle 80m and 384squre respectively find the length and breath of rectangle
Answers
Given
Perimeter of Rectangular playground is 80m
Area of Rectangular playground is 384m²
To Find
Length and breadth of the Rectangular playground
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