Question

The diagram represents a triangle that is reduced by a scale factor of 0.4.

A rectangle has a base of 6 inches and a height of 2 inches.

What is the height of the original triangle?
0.8 inches
2.4 inches
5 inches
8 inches

Answer 1

To find the height of the original triangle when it has been reduced by a scale factor of 0.4, we can set up the relationship between the dimensions of the original triangle and the reduced triangle.

Let \( h \) be the height of the original triangle. When the triangle is reduced by a scale factor of 0.4, the height of the reduced triangle becomes:

\[
\text{Height of reduced triangle} = h \times 0.4
\]

We need to compare the reduced triangle to the given rectangle, which has a height of 2 inches. To find the height of the original triangle, we will consider the height of the reduced triangle (which must be equal to the height of the rectangle).

Thus, we have:

\[
h \times 0.4 = 2
\]

Now, we can solve for \( h \):

\[
h = \frac{2}{0.4}
\]

Calculating the right side gives:

\[
h = \frac{2}{0.4} = \frac{20}{4} = 5
\]

Thus, the height of the original triangle is \( \boxed{5} \) inches.