Question

A rectangular counter is covered with 600 square tiles. The counter could have been covered with 400 tiles 1 cm longer on a side. Find the length of a side of the smaller tile

Answer 1

Answer:

Step-by-step explanation:

no of tiles =600 square tile

let x be the side of square tile

area = 600 x²

the counter could have been covered with 400 tiles 1cm longer a side

area = 400 (x+1)²

solving the two areas

600x²=400(x+1)²

600x²= 400(x² +2x +1)

600x²-400x²-800x -400 =0

200x²-800x -400 =0

x²-4x-2 =0

x²-4x+4-6 =0

x²-4x+4 =6

(x-2)(x-2) = 6

(x-2)²=6

x= 2+√6

x=4.449cm