Question

the perimeters of two squares are 60meters and 144 metres respectively. find the perimeter of another square equal in area to the sum of the first two squares

Answer 1

Solution ;

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Given :

   The perimeters of two squares are : 60 m & 144 m respectively,.

To Find :

    The perimeter of another square equal to the sum of the areas of first two squares,.

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We know that,

⇒ Perimeter of square = 4a,.

∴ Perimeter of 1st square = 60 m

⇒ 4a = 60

⇒ a = 15 m

∴ Length of the side of 1st square is 15 m

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⇒ Perimeter of 2nd square = 144 m

⇒ 4a = 144

⇒ a = 36 m

 ∴ The length of the side of 2nd square is 36 m
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Remember,

We need to find the perimeter of the square whose area is sum of the area of the two squares,.

⇒ Area of 1st square + Area of 2nd Square = Area of the square => which we need to find,.

 We know that,

⇒ Area of square = a²

Hence,

⇒ 15² + 36² = A² (let length of the side of the square = A)

⇒ 225 + 1296 = A²

⇒ 1521 = A²

⇒ A = √1521

⇒ A = √(39 × 39)

⇒ A = 39 m

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Perimeter of this square = 4a,

By substituting the value of a (a = 39, here)

We get,

⇒ 4(39)

⇒ 156 m

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       ∴ The perimeter of the square whose area is the sum of the areas of two squares is 156 m.

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                                Hope it Helps !!

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