Triangle Area and Rate of Change

The video tutorial explains how to determine the rate at which the base of a triangle changes when given the rates of change for the triangle's altitude and area. It starts with a problem statement, sketches the triangle, and introduces the area formula. The tutorial then reviews the given data, calculates the base length, and uses differentiation and the product rule to find the rate of change of the base. Finally, it substitutes the known values into the equation and solves for the rate of change, concluding with a summary of the findings.

What is the rate at which the height of the triangle is increasing?

• 4.0 cm/min

• 3.0 cm/min

• 2.5 cm/min

• 1.5 cm/min

What is the formula used to calculate the area of a triangle?

• Area = base x height

• Area = 1/2 x base x height

• Area = base - height

• Area = base + height

What is the value of DA/DT given in the problem?

• 2 cm²/min

• 5 cm²/min

• 3 cm²/min

• 4 cm²/min

Given the height is 12 cm and the area is 84 cm², what is the length of the base?

• 14 cm

• 12 cm

• 16 cm

• 10 cm

What is the calculated value of the base when the height is 12 cm and the area is 84 cm²?

• 10 cm

• 12 cm

• 14 cm

• 16 cm

What mathematical technique is used to differentiate the area formula with respect to time?

• Implicit Differentiation

• Quotient Rule

• Integration

• Chain Rule

Which rule is applied to differentiate the product of base and height?

• Quotient Rule

• Sum Rule

• Product Rule

• Difference Rule

What is the rate of change of the base when the height is 12 cm and the area is 84 cm²?

• -3.5 cm/min

• 3.5 cm/min

• 2.417 cm/min

• -2.417 cm/min

What is the significance of a negative DB/DT value?

• The base is zero

• The base is decreasing

• The base is constant

• The base is increasing

What is the purpose of substituting known values into the differentiated equation?

• To find the perimeter

• To find the area

• To find the rate of change of the base

• To find the height