Fangfang's shop is going to be renovated. Dad ordered a batch of square floor tiles. If you put them together and make them into a rectangle with an aspect ratio of 5: 4, there are still 34 pieces left. Please look at the supplementary questions. Solution: When spelling out a rectangle with an aspect ratio of 5: 4, the length is a block. According to the meaning of the question, the width is 4/5 of the length, and the width is 4/5a, which is 0.8a block.

Fangfang's floor tile = length x width +34 pieces =ax0.8a+34=0.8a? +34 ( 1)

In addition, the title tells us that if we change to a large rectangle with increased length and width, we will lose 57 pieces. Then the finished length =a+ 1, the finished width =0.8a+ 1, and the number of rectangular floor tiles = (a+1) x (0.8a+1) = 0.8a? + 1.8a+ 1

So Fangfang's father's floor tile = 57 rectangular floor tiles are missing after the spelling =(0.8a? + 1.8a+ 1)-57=0.8a？ + 1.8a-56(2)

In this way, (1) and (2) have an equivalent relationship, that is, 0.8a? +34 = 0.8a？ +1.8a-56, a=50 (square)

Substitute a into (1) or (2), that is, the number of floor tiles decided by Fang Fang =0.8a? +34=2034 (block)

Thank you for your wonderful question. I hope it will be adopted. Good luck!