Question

The length of the base of a triangle with a constant area varies inversely as the height. When the base is 10 inches long, the height is 6 inches. Formulate an equation involving inverse variation. (1 point)
Responses

b=60h
b equals 60 over h

h=b60
h equals b over 60

b=h60
b equals h over 60

b=60h

Answer 1

Inverse variation means that one quantity varies inversely as another, which can be represented as:

\[ b \cdot h = k \]

where \( b \) is the base, \( h \) is the height, and \( k \) is a constant.

From the problem, we know that when the base \( b \) is 10 inches and the height \( h \) is 6 inches, we can find the constant \( k \):

\[
k = b \cdot h = 10 \cdot 6 = 60
\]

Thus, the equation involving inverse variation is:

\[
b \cdot h = 60
\]

From this equation, we can express \( b \) in terms of \( h \):

\[
b = \frac{60}{h}
\]

So the correct response is:

**b equals 60 over h**.