Solve the Problem $7 \mathrm {~cm} \times 6 \mathrm {~cm}$ Find the Rate at Which the Area of the Zoom

Multiple Choice

Solve the problem. Round your answer, if appropriate.
-As the zoom lens in a camera moves in and out, the size of the rectangular image changes. Assume that the current image is $7 \mathrm {~cm} \times 6 \mathrm {~cm}$ . Find the rate at which the area of the image is changing $( \mathrm { dA } / \mathrm { df } )$ if the length of the image is changing at $0.5 \mathrm {~cm} / \mathrm { s }$ and the width of the image is changing at $0.4 \mathrm {~cm} / \mathrm { s }$ .

A) $11.6 \mathrm {~cm} ^ { 2 } / \mathrm { sec }$
B) $11.8 \mathrm {~cm} ^ { 2 } / \mathrm { sec }$
C) $5.8 \mathrm {~cm} ^ { 2 } / \mathrm { sec }$
D) $5.9 \mathrm {~cm} ^ { 2 } / \mathrm { sec }$