the perimeter and area of a rectangular play ground are 80m and 384m2 respectively find the length and breadth of the play ground
Answers
Given : perimeter and area of a rectangular play ground are 80m and 384m²
To Find : length and breadth of the play ground
Solution:
let say Length = x m
Breadth = B m
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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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.
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