The perimeters of two squares are 40 and 96

Question:

The perimeters of two squares are 40 and 96 metres respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Solution:

From the question it is given that,

Perimeters of first squares = 40m

Perimeter of second square = 96m

Let us assume side of first square = x1

and assume side of second square = x2

WKT, perimeter of first square = 4 × side

40 = 4x1

X1 = 40/4

X1 = 10 m

Then,

Perimeter of second square = 4 × side

96 = 4x2

X2 = 96/4

X2 = 24 m

As per the condition given in the question area of another square is equal to the first two squares.

Let us assume y2 be the area of another square.

So,

y2 = x12 + x22

y2 = 102 + 242

y2 = 100 + 576

y = √(676)

y = 26 m

Then,

Perimeter of another square = 4 × side

= 4 × y

= 4 × 26

= 104 m

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