Question

A garden is √30m long and √8 m wide. The garden is covered in grass except for a small rectangular pond which is √2 m long and √6 m wide. Express the area of the pond as a percentage of the area of the garden​

Answer 1

Step-by-step explanation:

Given :-

A garden with √30m long and √8 m wide

A small rectangular pond with √2 m long and √6 m wide.

To find :-

Express the area of the pond as a percentage of the area of the garden.

Solution :-

Given that

Length of a garden = √30 m

Breadth of the garden = √8 m

We know that

Area of a rectangle = length × breadth sq.units

Area of the rectangular garden

=> A = √30 × √8 m²

=> A = √(30×8) m²

=> A = √240 m²

Area of the rectangular garden

= √240 m²

Length of a rectangular pond = √2 m

Breadth of the rectangular pond = √6 m

We know that

Area of a rectangle = length × breadth sq.units

Area of the rectangular pond

=> √2 × √6 m²

=> √(2×6) m²

=> √12 m²

Area of the rectangular pond = √12 m²

Let X% of the area of the rectangular garden be the area of the pond

=> X% × √240 = √12

=> X% = √12/√240

=> X% = √(12/240)

=> X% = √(1/20)

=> X/100 = √(1/20)

On squaring both sides then

=> X²/10000 = 1/20

=> X² = 10000/20

=> X² = 500

=> X = √500

=> X = √(5×100)

=> X = 10×√5

We know that

√5 = 2.236

=> X = 10×2.236

=> X = 22.36 %

=> X = 22.36 %

Therefore,

The required percentage = 22.36%

Answer :-

The area of the pond is 22.36% of the area of the garden

Used formulae:-

→ Area of a rectangle = length × breadth sq.units

→ √5 = 2.236

→ √a×√b = √(ab)

→ √a / √b = √(a/b)

Answer 2

QUESTION :

• A garden is √30m long and √8 m wide. The garden is covered in grass except for a small rectangular pond which is √2 m long and √6 m wide. Express the area of the pond as a percentage of the area of the garden

GIVEN :

• A garden is √30m long and √8 m wide

• The garden is covered in grass except for a small rectangular pond which is √2 m long and √6 m

TO FIND :

• Express the area of the pond as a percentage of the area of the garden = ?

SOLUTION :

Garden length = 30 m

Garden width = 8 m

then, we have formula :

• rectangle = l × b

• Garden area = √30 × √8

• Garden area = √(30×8) metre

• Garden area = √240 metre

so, we have garden area = 240 metre

then, we have :

pond length = 2 m

pond width = 6 m

• pond area = √2 x √6 metre

• pond area = √(2×6) metre

• pond area = =√12 metre

so, we have pond area = √12 metre

then, we will using value of a to do this :

• a % × √ 240 = √12

• a % = √ 12 / √240

• a % = √(12/240)

• a % = √(1/20)

• a / 100 = √(1/20)

then, we will substitute the value :

• a²/10000 = 1/20

• a² = 10000/20

• a² = 500

• a = √500

• a = √(5×100)

• a = 10x√5

then, we have :

• 5 = 2.236

• a = 10 × 2.236

• a = 22.36 %

• a = 22.36 %

percentage of the area of the garden = 22.36 %