Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. the area of a triangle varies jointly with the height of the triangle and the length of its base. the area of one triangle is 150 square centimeters when its height is 20 centimeters and its base length is 15 centimeters. what is the area of a triangle having a height of 30 centimeters and a base length of 18 centimeters? 540 square centimeters 1080 square centimeters 300 square centimeters 270 square centimeters

Explanation:

Step1: Define joint variation formula

The area \( A \) of a triangle varies jointly with height \( h \) and base \( b \), so \( A = kbh \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

Given \( A = 150 \), \( h = 20 \), \( b = 15 \). Substitute into \( A = kbh \):
\( 150 = k \times 15 \times 20 \)
\( 150 = 300k \)
Solve for \( k \): \( k = \frac{150}{300} = \frac{1}{2} \).

Step3: Calculate the new area

Now, \( h = 30 \), \( b = 18 \), \( k = \frac{1}{2} \). Use \( A = kbh \):
\( A = \frac{1}{2} \times 18 \times 30 \)
\( A = 9 \times 30 = 270 \).

Answer:

270 square centimeters