Question

The length of each side of square A is
12 cm and that of square B is 9 cm.
What is the ratio of the area of square A
to that of square B?
A
9:16
B
16:9
С
4:3
D
3:4
Report​

Answer 1

Answer :

Option (B)

Ratio of the area of square A to the square B = 16 : 9

Given :

• Side of the square A = 12 cm
• Side of the square B = 9 cm

To find :

• Ratio of the area of square A to the square B

Knowledge Required :

Formula to calculate the area of square :-

• Area of square = a²

where,

• a denotes the side of the square

Solution :

Calculating the area of square A :-

⇒ Area of square (A) = a²

⇒ Substituting the given values :-

⇒ Area of square = (12)²

⇒ Area of square = 144

Area of the square (A) = 144 cm²

Now, calculating the area of square B :-

⇒ Area of square (B) = a²

⇒ Substituting the given values :-

⇒ Area of square = (9)²

⇒ Area of square = 81

Area of the square (B) = 81 cm²

Ratio of the area of square A to the square B :-

⇒ Ratio = Area of square (A) ÷ Area of square (B)

⇒ Ratio = 144/81

⇒ Ratio = 48/27

⇒ Ratio = 16/9

Therefore, the ratio of the area of square A to the square B = 16 : 9

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Some related formulae :-

• Perimeter of square = 4 × side
• Diagonal of square = √2a
• Area of rectangle = l × b
• Perimeter of rectangle = 2(l + b)
• Diagonal of rectangle = √l² + √b²
• Total surface Area of cuboid = 2(lb + bh + hl)
• Volume of cuboid =  length × breadth × height
• Perimeter of cuboid = 4 (length + breadth + height)
• Total surface area of cube = 6 × side²
• Volume of cube = side³
• Perimeter of cube = 12 × side