Question

sum of areas of two squares is 400 cm 2 .If the difference in their perimeters is 16cm. find the sides of the two squares

Answer 1

Heya !!!



Let the side of first and second square be X cm and Y cm.




Area of first square (A1) = (X)²



And,


Area of second square ( A2 ) = (Y)²

According to question,


Area of two square's = 400 cm²



Area of first square + Area of second square = 400


X² + Y² = 400 ---------(1)


------------------------------------


Perimeter of first square = 4X cm


And,


Perimeter of second square = 4Y cm



According to question,



Difference of their perimeter = 16 cm

4X - 4Y = 16


4 ( X - Y ) = 16


X - Y = 4 ---------(2)


From equation (2) we get,


X - Y = 4


X = ( 4 + Y ) --------(3)



Putting the value of X in equation (1)


X² + Y² = 400



( 4 + Y )² + Y² = 400



Y² + 16 + 8Y + Y² = 400



2Y² + 8Y - 400 + 16 = 0


2Y² + 8Y -384 = 0



2 ( Y² + 4Y - 192) = 0



Y² + 4Y - 192 = 0



Y² + 16Y - 12Y - 192 = 0



Y ( Y + 16 ) - 12 ( Y + 16 ) = 0


( Y + 16 ) ( Y - 12 ) = 0




( Y + 16 ) = 0 OR ( Y - 12 ) = 0



Y = -16 OR Y = 12






Putting Y = 12 in equation (3)



X = ( 4 + Y ) = 4+12 = 16 cm



Side of first square = X = 16 cm



And,



Side of second square = Y = 12 cm



★ HOPE IT WILL HELP YOU ★

Answer 2

here is your answer.

suppose area of two squares are x² and y².

a/q,
x²+y² =400
and,
x-y =4.
after solving this you will get side = 16 and 12.

Hope it helps you