How Fast is the Area of an Equilateral Triangle Changing?

  • Context: Undergrad 
  • Thread starter Thread starter Peppy
  • Start date Start date
  • Tags Tags
    Change
Click For Summary
SUMMARY

The discussion focuses on calculating the rate of change of the area of an equilateral triangle as its height increases. The height (h) is increasing at a rate of 3 cm/min, and the area (A) is expressed as a function of height. By applying the chain rule, the formula for the rate of change of area, dA/dt, is established as dA/dt = (dA/dh) * (dh/dt). The specific values for height and area are also addressed, with h set at 5 cm.

PREREQUISITES
  • Understanding of calculus, specifically the chain rule
  • Knowledge of the formula for the area of an equilateral triangle
  • Familiarity with derivatives and their applications
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the formula for the area of an equilateral triangle: A = (sqrt(3)/4) * h^2
  • Learn how to apply the chain rule in calculus
  • Explore examples of related rates problems in calculus
  • Investigate the implications of changing dimensions on geometric properties
USEFUL FOR

Students studying calculus, mathematics educators, and anyone interested in the application of derivatives to geometric problems.

Peppy
Messages
2
Reaction score
0
I need help with the question: The height h of an equilateral triangle is increasing at a rate of 3cm/min. How fast is the area changing when h is 5 cm.
 
Physics news on Phys.org
What's the area?What's the height?Can u write the former as a function of the latter?

Daniel.
 
You want [itex]dA/dt[/itex]. Use the chain rule:

[tex]\frac{dA}{dt} = \frac{dA}{dh} \frac{dh}{dt}[/tex]

Of course, you'll need to work out what the two derivatives on the right are.
 

Similar threads

Find the limit of the sum of the areas of all these triangles
  • · Replies 7 ·
Replies
7
Views
2K
MHB Help on Related Rates implicit differentiation
  • · Replies 5 ·
Replies
5
Views
3K
MHB Problem about equilateral triangles
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Proof that lattice points can't form an equilateral triangle
  • · Replies 5 ·
Replies
5
Views
5K
MHB How Fast is the Height of a Gravel Cone Increasing?
  • · Replies 2 ·
Replies
2
Views
3K
High School Area Increasing as a linear dimension increases -- Looking for intuition on this
  • · Replies 11 ·
Replies
11
Views
2K
MHB Angelina Lopez's Calculus Questions on Differentiation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Limits confusion -- What is meant by "instantaneous rate of change"?
  • · Replies 18 ·
Replies
18
Views
3K
MHB How Fast Does the Area of a Triangle Change with Increasing Angle?
  • · Replies 5 ·
Replies
5
Views
3K
MHB How fast is the surface area increasing
  • · Replies 4 ·
Replies
4
Views
2K