Question

The perimeters of two squares are 84 and 112 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Answer 1

AnswEr :

Perimeters of both squares 85 & 112 metres. We've to find the perimeter of another square equal in area to the sum of the first two squares.

⠀⠀⠀⠀From 1st square :

Formula of square's perimeter = 4(a)

↬ 4(a) = 84⠀{Perimeter of first square is 84m}

↬ a = 84/4

↬ a = 21 m

⠀⠀⠀⠀From 2nd Square :

Formula of square's perimeter = 4(a)

↬4(a) = 112 ⠀{Perimeter of first square is 112m}

↬a = 112/4

↬a = 28 m

⠀⠀⠀

⠀⠀⠀⠀⠀⛬ Here, we get length of both the square is 21 & 28 cm.

________________________________

⠀⠀⠀⠀Finding Areas :

Formula to find the area of sqaure is a².

Adding both squares lengths :

⠀⠀⠀⠀

↬ a² = (21)² + (28)²

↬ a² = 441 + 784

↬ a² = 1225

↬ a = √1225

↬ a = 35 m

⠀⠀⠀⠀

⠀⠀⠀⛬ Here, we get value of the a is 35 m.

Now, Putting the value of a in the formula of Perimeter of Square.

↬ Perimeter = 4(35)

↬ Perimeter = 140 m

⠀⠀⠀⠀⠀⠀⠀⠀So, the perimeter of another square equal in area to the sum of the first two squares is 140 m.

_______________________________

⠀⠀⠀⠀⠀⠀⠀⠀Used Formulas -

• Perimeter of the square = 4(a)
• Area of the square = a²

Answer 2

$\underline{\underline{\blue{\textbf{Step - By - Step - Explanation : -}}}}$

To Find :

• we need to find the perimeter of square is formed by Sum of areas of both squares.

Solution :

• perimeter of 1st circle = 84m
• perimeter of 2nd circle = 112m

$\boxed{\underline{\red{\textbf{Perimeter of square = 4 × side }}}}$

Perimeter of 1st square is 84m

›› 4 × side = 84

›› side = 84/4

›› side = 21 m

$\purple{\textrm{Side of 1st square = 21m}}$

Area of 1st square = side²

= 21²

= 441 m²

Perimeter of 2nd square is 112m

›› 4 × side = 112

›› side = 112/4

›› side = 28 m

Area of 2nd square :-

= 28²

= 28 × 28

= 784 m²

Now,

As we know that,

Area of third square is equal to the sum of areas of 1st 2 Squares

›› a² = 441 + 784

›› a² = 1225

›› a = √1225

›› a = 35 m

$\purple{\textrm{Side of third square = 35 m}}$

Perimeter of 3rd square :

= 4 × side

= 4 × 35

= 140 m

$\large\dag \large { \orange{\underline{\bf{Hence }}}}$

$\pink{\textrm{Perimeter of third square is 140m}}$

━━━━━━━━━━━━━━━━━━━━━━━━━