Question

6. The areas of two squares are in the ratio 225 : 256. What is the ratio of their perimeters?​

Answer 1

Given :-

◉ Ratio of area of two square = 225 : 256

To Find :-

◉ Ratio of perimeters

Solution :-

Let the common factor of both the areas of the two squares be x

Then,

• Area of square A = 225x
• Area of square B = 256x

We know,

⇒ Area of Square = (Side)²

Square A :-

⇒ Area = 225x

⇒ (side₁)² = 225x

⇒ side₁ = 15√x ...(1)

Square B :-

⇒ Area = 256x

⇒ (side₂)² = 256x

⇒ side₂ = 16√x ...(2)

Now,

⇒ Perimeter = 4 × Side

Square A :-

⇒ Perimeter₁ = 4 × 15√x [ from (1) ]

⇒ Perimeter₁ = 60√x ...(3)

Square B :-

⇒ Perimeter₂ = 4 × 16√x [ from (2) ]

⇒ Perimeter₂ = 64√x ...(4)

So,

⇒ Ratio of perimeters = (3) / (4)

⇒ Ratio = 60√x / 64√x

⇒ Ratio = 60/64

⇒ Ratio = 15/16

Hence, The ratio of thier perimeters is 15 : 16

Some Information :-

◉ Perimeter of a figure is the sum of all the sides of that figure.

◉ Perimeter of Rectangle = 2(Length + Breadth)

◉ Area of Rectangle = Length × Breadth

Answer 2

Step-by-step explanation:

Given that the areas of two squares are in the ratio 225 : 256.

We have to find the ratio of their perimeters.

Area of square = (side)²

Case 1)

Area of first square = (side)²

225 = (side)²

15 = side

Case 2)

Area of second square = (side)²

256 = (side)²

16 = side

Now,

Perimeter of square = 4 × side

Case 1)

Perimeter of first square = 4 × 15

= 60 .............(1)

Case 2)

Perimeter of second square = 4 × 16

= 64 ............(2)

Therefore,

(Perimeter of first square)/(Perimeter of second square) = 60/64

= 60/64 × 4/4 = 15/16

Hence, the ratio of their perimeters is 15:16.