Math Problem Statement

The figures below are similar. Use proportions to find the length of m.

Solution

To solve for mm, we can set up a proportion based on the similarity of the two triangles. In similar triangles, corresponding side lengths are proportional. The sides labeled in the small triangle are 4 and mm, and in the larger triangle, they are 10 and 15.

Steps to solve for mm:

  1. Set up the proportion: m4=1510\frac{m}{4} = \frac{15}{10}

  2. Simplify the right side of the proportion: 1510=32\frac{15}{10} = \frac{3}{2}

    So the proportion becomes: m4=32\frac{m}{4} = \frac{3}{2}

  3. Cross-multiply to solve for mm: 2m=4×32m = 4 \times 3 2m=122m = 12

  4. Divide by 2: m=6m = 6

Answer:

m=6m = 6

Would you like more details or have any questions?


Here are 5 related questions that expand on this concept:

  1. How would you solve for mm if the larger triangle had different side lengths?
  2. What are other ways to check if two triangles are similar besides using side lengths?
  3. How can you use proportions to find unknown lengths in non-triangular similar shapes?
  4. What if both triangles had all unknown side lengths but shared a scale factor? How would you approach this?
  5. Can proportions be used to solve problems in three-dimensional figures?

Tip: Remember that similar figures have corresponding angles that are equal and corresponding sides that are proportional!

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Math Problem Analysis

Mathematical Concepts

Geometry
Proportions
Similar Figures

Formulas

m / 4 = 15 / 10

Theorems

Properties of Similar Triangles

Suitable Grade Level

Grades 7-8