abcd is a square. inside the square abcd there are yellow tiles and red tiles. red tiles are among the diagonals of the square. dimensions of the red tiles and yellow tiles are 4cm *4cm and 1cm*1cm. if there are 61 red tiles, then what is the number of yellow tiles?
Answers
Answer:
14400 yellow tiles
Step-by-step explanation:
if there are 61 red tiles diagonally then there will 1 red tile in centre and other 60 tiles will be arranged in such a way as drawn in photo.
diagonal of each red tile= √4^2+4^2. ( by
Pythagoras
theorem)
= 4√2 cm
diagonal of the square ABCD= diagonal of one
tile × no. of tile in one
diagonal of square
=4√2 × (15+15+1)
=4√2 × 31
=124√2 cm
area of square= diagonal^2/2
= 124√2^2/2
= 15376 cm^2
area of each red tile=4×4=16cm^2
area occupied by 61 red tiles=16×61 = 976cm^2
area occupied by yellow tiles=15376-976= 14400
area of each red tile =1×1 = 1cm^2
no. of yellow tiles=14400/1 = 14400 yellow tiles
