Question

The perimeters of two squares are 80 cm and 64 cm. Find the perimeter of a<br />
third square whose area is equal to the difference of the areas of the two<br />
squares.​

Answer 1

Given:-

• Perimeter of 1st square = 80 cm
• Perimeter of 2nd square = 64 cm
• Area of thrid square is equal to the difference of the first and second square.

To Find:-

• Area of the third square.

Solution:-

For 1st square,

Perimeter = 80 cm

We know,

Perimeter of square = 4 × side

Hence,

80 = 4 × side

=> 80/4 = side

=> side = 20 cm

Now,

Area of square = (side)²

Therefore,

Area of 1st square = (20)² = 400 cm²

Therefore, area of the 1st square is 400 cm²

Now,

For 2nd square,

Perimeter = 64 cm

We know,

Perimeter of square = 4 × side

Hence,

64 = 4 × side

=> 64/4 = side

=> side = 16 cm

Now,

Area of square = (side)²

Therefore,

Area of 2nd square = (16)² = 256 cm²

Therefore the area of the 2nd square is 256 cm²

Now,

Difference between the area of 1st and 2nd square:-

= (400 - 256) cm² = 144 cm²

As it was said in the question the difference between the area of 1st and 2nd square is equal to the area of the 3rd square.

Hence the area of the third square is 144 cm²

Now,

Since the area of the third square is 144 cm²

We can find the side of the third square,

We know,

(Side)² = Area of the square

Hence,

(Side)² = 144

=> Side = √144

=> Side = 12 cm

Now,

Perimeter of the third Square:-

= 4 × side

= 4 × 12

= 48 cm

Hence the perimeter of the third square is 48 cm

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Formula Used:-

• Area of square = (side)² sq.units
• Perimeter of square = (4 × side) units

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Answer 2

☆Answer☆

Given:-

Perimeter of one square = 80 cm

Perimeter of another square = 64 cm

• Area of third square is equal to the difference of the 1st and 2and square.

To Find:-

Perimeter of third square.

Solution:-

Perimeter of 1st square = 80 cm

4×side = 80 cm

side = (80/4) cm

side = 20 cm

• Area of 1st square = side²

=> (20)² cm²

=> 400 cm²

Perimeter of 2nd square = 64 cm

4×side = 64 cm

side = (64/4) cm

side = 16 cm

• Area of 2nd square = side²

=> (16)² cm²

=> 256 cm²

Area of third square =

Area of 1st square + Area of 2nd square

=> (400-256) cm²

=> 144 cm²

• Area of third square = 656 cm²

=> (side)² = 656 cm²

=> side = 12 cm

Perimeter of third square

= 4×side

= (4×12) cm

= 48 cm

Hence, perimeter of third square is 48 cm.

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