Question

One diagonal of a rhombus is decreasing at a rate of 7 centimeters per minute and the other diagonal of the rhombus is increasing at a rete of 10 centimeters per minute. At a certain instant the decreasing diagonal is 4 centimeters and the increasing diagonal is 6 centimeters hat is the rate of change of the area of the rhombus at that instant in square centimeters per minute)?

a. 1
b. -16
c. -1
d. 16

Answer 1

c. -1

Explanation:

The area of a rhombus is given in terms of its diagonal lengths x and y as ...

A = (1/2)xy

Then the rate of change is ...

A' = (1/2)(x'y +xy')

For the given numbers, the rate of change is ...

A' = (1/2)((-7 cm/min)(6 cm) +(4 cm)(10 cm/min))

A' = (1/2)(-42 cm²/min +40 cm²/min)

A' = -1 cm²/min . . . . . matches choice C