In this page rate of change question5 we are going to see solution of some practice question of the worksheet.

**Question 5:**

The altitude of a triangle is increasing at a rate of 1 cm/min while the area of the triangle is increasing at a rate of 2 cm²/min. At what rate is the base of the triangle changing when the altitude is 10 cm and the area is 100 cm².

**Solution:**

Let "b" and "h" be the base and height of the triangle ABC

Area of triangle ABC

(A)= (1/2) b h

dh/dt = 1 cm/min

dA/dt = cm²/min

dh/dt = ?

h = 10 area = 100

100 = (1/2) x b x 10

b = (100 x 2)/10

b = 20

dA/dt = (1/2) [b (dh/dt) + h (db/dt)]

h (db/dt) = 2 (dA/dt) - b (dh/dt)

(db/dt) = (2/h) (dA/dt) - (b/h) (dh/dt)

(db/dt) = (2/10) (2) - (20/10) (1)

(db/dt) = (4/10) - (20/10)

(db/dt) = (4 - 20)/10

(db/dt) = - 16/10

(db/dt) = - 1.6 cm/min

- Back to worksheet
- First Principles
- Implicit Function
- Parametric Function
- Substitution Method
- logarithmic function
- Product Rule
- Chain Rule
- Quotient Rule
- Rolle's theorem
- Lagrange's theorem
- Finding increasing or decreasing interval
- Increasing function
- Decreasing function
- Monotonic function
- Maximum and minimum
- Examples of maximum and minimum