Question

the adjoining figures shows a set of concentric squares. if the diagonal of the innermost square is 2 unit and if the distance between the corresponding corners of any two successive squares is 1 unit, find the difference between the areas of the third and fifth squares, counting the innermost square

Answer 1

Answer:

Difference between the areas of 5th and 3rd square is 32 units

Step-by-step explanation:

Let di be the diameter of  ith square and d1 be diagonal of innermost square

Di= d1+(i-1)x2

 D3=d1+(3-1)x2 =2+2x2=6 units

 D5= 2+(5-1)x2= 10 units

Now, Area of a square =d^2/2

Area of 3rd square= d3^2/2

Area of 5th square= d5^2/2

Difference between the areas,

(d5^2/2)- (d3^2/2)= (10^2/2)-(6^2/2)

=50-18

=32 units

Difference between the areas of 5th and 3rd square is 32 units