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 solve by quadratic equation

Answer 1

The sum of areas of 2 squares is 400and the difference between their perimeters is 16cm. Find the sides of both squares.

Let side of 1st square=x cm.

∴ Area of 1st square=x²cm²

GIVEN, Sum of areas =400cm²

∴ Area of 2nd square=(400-x²)cm²

AND side of 2nd square=√[(20-x)² i.e.20-x .......(1)

Difference of perimeters=16cm.

THEN-

4x-4(20-x)=16 (ASSUMING THAT 1ST SQUARE HAS LARGER SIDE)

X=12

HENCE - SIDE OF 1ST SQUARE = 12CM ;

SIDE OF 2ND SQUARE=20-12=8CM. [FROM (1)]

WHICH IS NOT THE REQUIRED ANSWER AS SUM OF AREAS OF SQUARES OF FOUNDED SIDES IS NOT 400CM²

Hope This Helps :)