Question

The area of a square is three times the area of a given rectangle. The length of rectangle is 5 cm more than 5sq cm which is thrice its width. Find the perimeter of the square.​

Answer 1

The perimeter of square is 120 cm .

Step-by-step explanation:

Given as :

The area of a square is three times the area of a given rectangle

Let The length of rectangle = l cm

Let The width of rectangle = w cm

Let The each sides of a square = s cm

According to question

Area of rectangle = Length × breadth

i.e   A = l × b

Area of square = side × side

So, A' = s²

∵     area of a square is three times the area of rectangle

i.e    A' = 3 A

Or,  s² = 3 ( l b )                        ...............1

Again

Length  of rectangle is 5 cm more than 5 sq cm

i.e  l = 5 + 5²

∴    Length of rectangle = 30 cm

And

Length is thrice its width

i.e   l = 3 w

so,  30 cm = 3 w

∴            w = $\dfrac{30 cm}{3}$

i.e          w = 10 cm

Width of rectangle = 10 cm

From eq 1

∵    s² = 3 ( l b )    

So,  s² = 3 ( 30 cm × 10 cm )  

Or,    s² = 3 × 300 sq cm

Or,    s² = 900 sq cm

∴       s = $\sqrt{900}$ cm

i.e     s = 30 cm

So, The side of square = s = 30 cm

Again

Perimeter of square = 4 × side

P = 4 × 30 cm

∴  Perimeters = 120 cm

So, The perimeter of square = P = 120 cm

Hence, The perimeter of square is 120 cm . Answer