Question

A room has a perimeter of 52 ft. The length x is 6 ft greater than the width y. Which shows the correct system and the dimensions of the room?

A. 2x + 2y = 52; x + 6 = y + 6; x = 10 ft, y = 16 ft
B. 2x + 2y = 52; x + 6 = y; x = 16 ft, y = 10 ft
C. x + y = 52; x = y + 6; x = 22 ft, y = 28 ft
D. 2x + 2y = 52; x = y + 6; x = 16 ft, y = 10 ft

Answer 1

D. 2x + 2y = 52; x = y + 6; x = 16 ft, y = 10 ft

Explanation:

length x

width y

perimeter 2x + 2y

perimeter 52

2x + 2y = 52

length x is 6 ft greater than width y

x = y + 6

We need a system with equations

2x + 2y = 52

x = y + 6

2(y + 6) + 2y = 52

2y + 12 + 2y = 52

4y = 40

y = 10

Answer: D. 2x + 2y = 52; x = y + 6; x = 16 ft, y = 10 ft