Question

a large square region is paved with n^2 gray square tiles, each measuring s inches on a side .a border d inches wide surrounds each tile when n=24 the 576 gray tiles cover64% 0f area of larger square what is ratio of d/s

Answer 1

Answer:

Let we have square tiles of a certain length, which we will call

′

x

′

cm.

The area of each tile is x

2

cm

2

.

The total area paved would be 600x

2

cm

2

.

According to given question,

600x

2

=864(x−1)

2

⇒600x

2

=864x

2

−1728x+864

⇒264x

2

−1728x+864=0

⇒24(11x

2

−72x+36)=0

⇒11x

2

−66x−6x+36=0

⇒11x(x−6)−6(x−6)=0

⇒(x−6)(11x−6)=0

⇒x−6=0,11x−6=0

⇒x=6or

11

6

Hence, the length of tiles=x=6cm.

Hence, this is the answer.