Question

The perimeters of two squares are 848 cm and 436 cm. Find the perimeter of a square
whose area is equal to the sum of the areas of two squares,​

Answer 1

Answer:-

Let the side of the first square be x cm and the side of the second square be y cm.

Given:-

Perimeter of first square = 848 cm

We know that,

Perimeter of a square = 4 × side

⟹ 848 = 4 × x

⟹ 848/4 = x

⟹ 212 cm = x

Also given that,

Perimeter of second square = 436 cm.

⟹ 436 = 4 × y

⟹ 436/4 = y

⟹ 109 cm = y

And ;

Area of a square = Area of the first square + Area of the second square.

We know,

Area of a square = (side)²

So,

According to the above condition;

⟹ Area of the square = x² + y²

⟹ Area of the square = (212)² + (109)²

⟹ Area of the square = 44944 + 11881

⟹ Area of the square = 56825

⟹ (side)² = 56825

⟹ side = √56825

⟹ side = 238.37 cm

Now,

Perimeter of the square = 4 × side

Perimeter of the square = 4(238.37)

Perimeter of the square = 953.48 cm

∴ The perimeter of the required square is 953.48 cm.

Answer 2

Answer:

Given :-

• The perimeter of two squares are 848 cm and 436 cm.

To Find :-

• What is the perimeter of a square whose area is equal to the sum of the areas of two squares.

Solution :-

$\longmapsto$ Side of square of the perimeter 848 cm is :

As we know that,

$\sf\boxed{\bold{\pink{Side\: of\: Square =\: \dfrac{Perimeter}{4}}}}$

Given :

• Perimeter = 848 cm

$\implies \sf Side\: of\: Square =\: \dfrac{\cancel{848}}{\cancel{4}}$

$\implies \sf\bold{\green{Side\: of\: Square =\: 212\: cm}}$

Again,

$\longmapsto$ Side of square of the perimeter 436 cm is :

Given :

• Perimeter = 436 cm

$\implies \sf Side\: of\: Square =\: \dfrac{\cancel{436}}{\cancel{4}}$

$\implies \sf\bold{\green{Side\: of\: Square =\: 109\: cm}}$

Now, we have to find the total area of both square :

Again, as we know that,

$\sf\boxed{\bold{\pink{Area\: of\: Square =\: {(Side)}^{2}}}}$

Then,

$\implies \sf Total\: area\: of\: both\: square =\: {(212)}^{2} + {(109)}^{2}$

$\implies \sf Total\: area\: of\: both\: square =\: 44944 + 11881$

$\implies \sf{\bold{Total\: area\: of\: both\: square =\: 56825\: cm}}$

Again, we have to find the side of square :

Let, the side of square be x cm

According to the question,

$\implies \sf {x}^{2} =\: 56825$

$\implies \sf x =\: \sqrt{56825}$

$\implies \sf{\bold{x =\: 238.37\: cm}}$

Hence, the side of square is 238.37 cm.

Now, as we know that,

$\sf\boxed{\bold{\pink{Perimeter\: of\: square =\: 4 \times Side}}}$

Given :

• Side = 238.37 cm

Then,

$\implies \sf Perimeter\: of\: Square =\: 4 \times 238.37$

$\implies \sf\bold{\red{Perimeter\: of\: Square =\: 953.48\: cm}}$

$\therefore$ The perimeter of a square is 953.48 cm.