1. A dance floor is made from square wooden tiles with a side length of 1 foot. The floor can be laid out as a square or a rectangle. The width of the rectangular floor is 10 feet less than the width of the square floor, and its length is 15 feet greater than the length of the square floor.

a) How much greater is the length of the rectangular dance floor than the width?

b) The perimeter of the rectangular dance floor is 130 feet. What are the length and width of the dance floor?

c) How many square tiles make up the dance floor?

legnth/width for square = x
width of rectangle= x-10
legnth of rectangle=x+25
so (x-10)+35=2x+25 which is the first part
part two
the perimiter of rectangle floor =130
perimiter= 2width+2legnth so 130/2=width+height
width=x-10 and legnth=x+25 so
x-10+x+25=130/2
2x+15=75
minus 15 from both sides
2x=60
divide by two
x=60 which is legnth/width of the square, but we want the legnth and width of the rectangle so
x-10=width=50
x+25=legnth=85
so the number of tiles on the floor is 50 times 85 which is 4250 tiles

Answered by celestialglow | 2024-06-13

The length of the rectangular dance floor is 25 feet greater than its width. The dimensions of the rectangular floor are 45 feet in length and 20 feet in width, making a total of 900 square tiles on the dance floor.
;

Answered by celestialglow | 2025-05-16