Math Problem Statement

Find the missing side length of similar triangles based on the given sides.

Solution

The image shows a math problem involving similar figures, specifically comparing two triangles to find a missing side length. Here's a detailed solution for the problem:

Problem Analysis:

  1. The problem involves two similar triangles:
    • Triangle 1: Sides are given as 18 (height) and 24 (base).
    • Triangle 2: One side length is missing (denoted as "x"), and the other given side is 40.

Solution:

Since the triangles are similar, their corresponding sides are proportional. This means the ratio of the sides of the first triangle will be the same as the ratio of the sides of the second triangle.

Set up the proportion using the sides: 18x=2440\frac{18}{x} = \frac{24}{40}

Cross-multiply to solve for xx: 18×40=24×x18 \times 40 = 24 \times x

720=24x720 = 24x

Now, solve for xx: x=72024x = \frac{720}{24}

x=30x = 30

Answer:

The missing side length xx is 30 units.


Would you like further details or have any questions about this solution?

Related Questions:

  1. What are similar triangles, and how do their properties help in solving problems like this?
  2. How do you determine if two triangles are similar based on side lengths and angles?
  3. Can the method of setting proportions be used for figures other than triangles?
  4. How do scaling factors affect the dimensions of similar geometric figures?
  5. What are other real-world applications of similar triangles in measurements?

Tip: Always check if the triangles are similar by comparing their corresponding angles or side ratios before setting up proportions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Similar Triangles
Proportions

Formulas

Ratio of corresponding sides in similar triangles

Theorems

Triangle Similarity Theorem

Suitable Grade Level

Grades 7-9