Question

the perimeter of a rectangular garden is 50m and its area is
$150m {}^{2}$
CALCULATE GARDENS LENGTH AND BREADTH
​

Answer 1

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

$\sf{2(x + y) = 50}$

$\implies \: \sf{(x + y) = 25 \: \: \: - - - - (1)}$

Area = xy m²

So by the given condition

$\sf{xy = 150 \: \: \: - - - - - (2)}$

Using Equation 1 we get

$\sf{x(25 - x) = 150}$

$\sf{ \implies \: {x}^{2} - 25x + 150 = 0}$

$\sf{ \implies \: {x}^{2} - 15x - 10x + 150 = 0}$

$\sf{ \implies \: (x - 15)(x - 10)= 0}$

$\sf{ \implies \: x = 15 \: ,\: 10}$

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

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Answer 2

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

2(x+y)=50

⟹(x+y)=25−−−−(1)

Area = xy m²

So by the given condition

xy=150−−−−−(2)

Using Equation 1 we get

x(25 - x) = 150}x(25−x)=150

⟹x² −25x+150=0

⟹x² −15x−10x+150=0

⟹(x−15)(x−10)=0

⟹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

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