Question 79323
A square room has a square rug in it. The area of the room not covered by the rug is 51 sq feet. The sum of the length of a side of the rug and the length of a side of the room is 17 feet. Find the dimensions of the room.
:
Let x = 1 side of the room
Then x^2 = area of the room
:
Let (17-x) = 1 side of the square rug
Then (17-x)^2 = area of the rug
:
Room area - rug area = 51 sq/ft
x^2 - (17-x)^2 = 51
:
x^2 - (289 - 34x + x^2) = 51; FOILed (17-x)(17-x)
:
x^2 - 289 + 34x - x^2 = 51; Removed the brackets, changed the signs
:
34x = 51 + 289; x^2's eliminated, added 289 to both sides
:
34x = 340
:
x = 340/34
:
x = 10 ft is the side of the room
:
17 - 10 = 7 ft is the side of the rug
:
:
Check, room area - rug area
10^2 - 7^2 = 51