Math Problem Statement

This pair of figures is similar. Find the value of the missing side (x).

Solution

To find the value of the missing side xx in the similar triangles, we can use the property that the ratios of corresponding sides of similar triangles are equal.

Given triangles:

  • Larger triangle sides: 12, 20
  • Smaller triangle sides: 3, xx

The ratio of the corresponding sides should be equal. Therefore, we can set up the following proportion:

123=20x\frac{12}{3} = \frac{20}{x}

Now, solve for xx:

  1. Simplify the ratio on the left side:

123=4\frac{12}{3} = 4

  1. Set up the equation:

4=20x4 = \frac{20}{x}

  1. Cross-multiply to solve for xx:

4x=204x = 20

  1. Divide both sides by 4:

x=204=5x = \frac{20}{4} = 5

So, the value of the missing side xx is 55.

Would you like any more details or have any questions?

Here are 5 related questions that expand on this information:

  1. What are the properties of similar triangles?
  2. How can you verify that two triangles are similar?
  3. How do you find the scale factor between two similar triangles?
  4. Can the method used here apply to other geometric shapes? If so, how?
  5. How does changing the lengths of sides in one triangle affect the other in similar figures?

Tip: When working with proportions, always ensure the ratios are set up with corresponding sides from each figure or shape.

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Math Problem Analysis

Mathematical Concepts

Similar Triangles
Proportions

Formulas

Ratio of corresponding sides: (larger side in larger triangle / corresponding side in smaller triangle) = (other larger side in larger triangle / corresponding smaller side)

Theorems

Corresponding sides of similar triangles are proportional

Suitable Grade Level

Grades 6-8