Question

The perimeter of a square garden is 48 m . A small flower bed covers 18sq m area inside this garden. (a) what is the area of the garden that is not covered by the flower bed ? (b) what fractional part of the garden is covered by flower bed ? (c) find the ratio of the area covered by the flower bed and the remaining area .

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Answer 1

Required Answers :

(a) The answer is as follows -

Given

• Perimeter of the square garden = 48 m

• Area of the small flower bed = 18 m²

To Find

• Area of the garden that is not covered by the flower bed

Formulae Used

• Perimeter of Square = 4 × side

• Area of Square = side × side

Solution

To find the area of the garden that is not covered by the flower bed we need to first find out the area of the square garden, so let's do it!

48 = 4 × side

48 = 4s

$\sf\dfrac{48}{4} = s$

$\sf\dfrac{\not48}{\not4} = 12$

$∴ \sf \: s = 12 \: m$

Now we have the side if the Square, let's find out the Area then!

Area of Square = side × side

Area of Square = 12 × 12

Area of Square = 144 m²

Now we have both, the area of the square garden and the area of the small flower bed, if we will subtract both of them, we will get the area of the garden that is not covered by the flower bed, so let's do it!

144 - 18 = 126 m²

Hence, Subtracted!

∴ Area of the garden that is not covered by the flower bed is 126 m²

(b) The answer is as follows -

The required fractional part of the garden which is covered by the flower bed :

$= \sf\dfrac{Area \: of \: the \: flower \: bed}{Area \: of \: the \: square \: garden}$

$= \sf\dfrac{18}{144}$

$= \sf\dfrac{1}{8}$ ( When simplified )

Final Answer - $\sf\dfrac{1}{8}$

(c) The answer is as follows -

The ratio of the area covered by the flower bed and the remaining area :

$= \sf\dfrac{Area \: of \: the \: flower \: bed}{Area \: of \: the \: garden \: that \: is \: not \: covered \: by \: the \: flower \: bed}$

$= \sf\dfrac{18}{126}$

$= \sf\dfrac{1}{7}$ ( When simplified )

$= \sf{1 : 7}$

Final Answer - $\sf{1 : 7}$

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Answer 2

Answer:

perimeter of square garden =48m

1 side length=48/4=12m

Area of garden = 144m2

Area of flower bed = 18m2

Area not covered by flowers = (144-18)m2 = 126m2

Fractional part covered by flower bed = 18/144 = 1/8

Ratio = 18 : 126 = 1 : 7