What is the area of the square is equal to the area of a rectangle whose measures are 16 cm and 9 cm find the perimeter of the square also find the ratio of length of diagonals of the square and rectangle

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Solution

Dear Student,
Area of square= area of rectangle
$s i d e^{2} = L e n g t h \times b r e a d t h s i d e^{2} = 16 \times 9 s i d e^{2} = 144 c m^{2} s i d e = 12 c m (R e j e c t i n g - 12 a s l e n g t h c a n n o t b e n e g a t i v e) P e r i m e t e r o f s q u a r e = 4 s i d e = 4 \times 12 = 48 c m D i a g o n a l o f s q u a r e = \sqrt{2} \times s i d e = 12 \sqrt{2} c m = 16.968 c m D i a g o n a l o f r e c \tan g l e = \sqrt{l e n g t h^{2} + b r e a d t h^{2}} = \sqrt{9^{2} + 16^{2}} = \sqrt{81 + 256} = \sqrt{337} c m = 18.35 c m$

$\frac{D i a g o n a l o f s q a u r e}{D i a g o n a l o f r e c \tan g l e} = \frac{16.968}{18.35} = 0.92468 : 1$
Regards

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