The length of rectangular garden is 50 m and breadth is 4 m find its perimeter
The perimeter of a rectangle is = 2 *(1 + b)=2 ( 1._ * 2)-2 __
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Answer:
SOLUTION
GIVEN
The perimeter of a rectangular garden is 50m and its area is 150 m²
TO DETERMINE
The length and breadth of the garden
EVALUATION
Let length = x cm and breadth = y cm
∴ Perimeter = 2( x + y) cm
So by the given condition
\sf{2(x + y) = 50}2(x+y)=50
\implies \: \sf{(x + y) = 25 \: \: \: - - - - (1)}⟹(x+y)=25−−−−(1)
Area = xy m²
So by the given condition
\sf{xy = 150 \: \: \: - - - - - (2)}xy=150−−−−−(2)
Using Equation 1 we get
\sf{x(25 - x) = 150}x(25−x)=150
\sf{ \implies \: {x}^{2} - 25x + 150 = 0}⟹x
2
−25x+150=0
\sf{ \implies \: {x}^{2} - 15x - 10x + 150 = 0}⟹x
2
−15x−10x+150=0
\sf{ \implies \: (x - 15)(x - 10)= 0}⟹(x−15)(x−10)=0
\sf{ \implies \: x = 15 \: ,\: 10}⟹x=15,10
From Equation 2
When x = 15 we have y = 10
When x = 10 we have y = 15
Since Length > Breadth
∴ x = 15 & y = 10
Hence Length = 15 m and Breadth = 10 m
Step-by-step explanation:
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Answer:
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