Question

In order to find the square of 53 by Visual method, find out the area of the yellow and purple shaded portions respectively.

• A. 2500 sq.units, 9 sq.units
• B. 9 sq. units, 2500 sq. units
• C. 150 sq. units, 9 sq.units
• D. 50 sq. units, 3 sq. units

Answer 1

The correct option is A 2500 sq.units, 9 sq.units

To find the square of 53, we split 53 into (50+3) and apply the identity $(a+b{)}^2$ = $a^2$ + 2ab + $b^2$
Hence ${53}^2$ = $(50+3{)}^2$ = $(50{)}^2$ + $2\times 50\times 3$ + $(3{)}^2$
The sides of the yellow square is 50 units. Hence, its area is 2500sq.units, while the sides of the purple square is 3 units.
Hence, its area will be = 9 sq .units.


The total area of the big square gives the value of ${53}^2$
${53}^2$ = $(50+3{)}^2$ = (2500 + $2\times 150$ + 9 ) = 2809 sq.units