The dimensions of a door are $4 \mathrm { ft }$ by $7 \mathrm { ft } 6 \text { in }$ . If the same amount is added to each dimension of the door, the area is increased by $19.5 \mathrm { ft } ^ { 2 }$ Find the dimensions of the new door.
A) $5.5 \mathrm { ft } \times 9 \mathrm { ft }$
B) $4.5 \mathrm { ft } \times 8 \mathrm { ft }$
C) $6.5 \mathrm { ft } \times 10 \mathrm { ft }$
D) $5.5 \mathrm { ft } \times 8.5 \mathrm { ft }$
E) $4.5 \mathrm { ft } \times 8.5 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The original area of the door is $4 \text{ ft} \times 7.5 \text{ ft} = 30 \text{ ft}^2$. The new area is $30 \text{ ft}^2 + 19.5 \text{ ft}^2 = 49.5 \text{ ft}^2$. The dimensions that give this area and are 1.5 ft larger in both dimensions than the original are $5.5 \text{ ft} \times 9 \text{ ft}$.

The Dimensions of a Door Are 4ft4 \mathrm { ft }4ft

The Dimensions of a Door Are $4 \mathrm { ft }$