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Question
The perimeter of a square is 128cm and that of another is 96cm. Find the perimeter and the diagonal of a square whose area is equal to the sum of the areas of these two squares.
Solution
The perimeter of a square with side s = p = 4s
∴ Here, the perimeter of the square are 128cm and 96cm
∴ the sides of the two squares are 32cm and 24cm
We know, The area of a square with side s = s2
∴ the areas of the two squares are = 32cm2 = 1024cm2 and 24cm2 = 576cm2
∴ the combined area
= area of the new square
= 1024cm2 + 576cm2
= 1600cm2
the side of the square
= `sqrt(1600)`
= 40cm
The perimeter of a square with side 40
= 4 x 40
= 160cm
The sides and diagonal of a square from a right triangle as each angle of a square is a right angle.
Diagonal is the side opposite to the right angle, therefore it is the hypotenuse
Here, diagonal of the square
= `sqrt(40^2 + 40^2)`
= `40sqrt(2)`
= 40(1.414)
= 56.57cm.
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