Consider the enlargement of the triangle.

A small triangle has a base of 1.7 feet and height of 9.3 feet. A larger triangle has a base of 3.5 feet and height of x feet.
Not drawn to scale

Rounded to the nearest tenth, what is the value of x?
15.8 feet
19.1 feet
23.3 feet
32.6 feet

To solve this problem, we will use the property of similar triangles, which states that corresponding sides of similar triangles are proportional. The base and height of the two triangles are proportional, so we can set up the following equation:

\[
\frac{\text{base of small triangle}}{\text{base of large triangle}} = \frac{\text{height of small triangle}}{\text{height of large triangle}}
\]

Substituting the known values:

\[
\frac{1.7}{3.5} = \frac{9.3}{x}
\]

Now, solve for \( x \):

1. Cross multiply to eliminate the fractions:
\[
1.7x = 3.5 \times 9.3
\]

2. Calculate the right-hand side:
\[
1.7x = 32.55
\]

3. Solve for \( x \):
\[
x = \frac{32.55}{1.7} \approx 19.1
\]

Thus, the value of \( x \), rounded to the nearest tenth, is **19.1 feet**.

Let me know if you'd like further details or have any questions!

Here are five related questions:
1. How do we know that the triangles are similar?
2. What is the general rule for solving problems with similar triangles?
3. How would the solution change if the base of the larger triangle were different?
4. Can you explain how cross-multiplication works in proportional relationships?
5. What happens to the height if the base of both triangles is doubled?

**Tip:** When working with proportions, cross-multiplying can make solving for an unknown easier, especially when fractions are involved.

A small triangle has a base of 1.7 feet and height of 9.3 feet. A larger triangle has a base of 3.5 feet and height of x feet. Rounded to the nearest tenth, what is the value of x? 15.8 feet, 19.1 feet, 23.3 feet, or 32.6 feet?

Solve a problem involving the enlargement of a triangle. Learn how to use the property of similar triangles to find the missing height of a larger triangle when given the base and height of a smaller triangle. Suitable for students in Grades 8-10.

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