question_answer

            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.

Answer:

Let the sides of two squares are a and b respectively.

4a = 40 and 4b = 96

\[\therefore \]      a = 10 m and b = 24 m

Given,

The perimeter of another square = Sum of area of two squares.

= Area of Ist square + Area of IInd square

\[={{a}^{2}}+{{b}^{2}}\]

\[={{\left( 10 \right)}^{2}}+{{\left( 24 \right)}^{2}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\]

=100 + 576

= 676 m2

Hence, the perimeter of another square = 676 m.