Question - Solving for Missing Side Length of Similar Triangles
Solution:
The triangles in the image are similar, which means their corresponding sides are proportional. From the image, we can set up a ratio of the corresponding sides of the two similar triangles.Let's denote the unknown side length of the smaller triangle as $$ x $$. We are given the sides of the larger triangle as 8 and 16. Since the triangles are similar, the ratio of the sides of the smaller triangle to the larger one should be the same.So we have:\[\frac{x}{8} = \frac{7}{16}\]Now we can solve for $$ x $$ by cross-multiplying:$$ 16x = 8 \times 7 $$$$ 16x = 56 $$Now, divide both sides by 16 to find $$ x $$:$$ x = \frac{56}{16} $$$$ x = 3.5 $$Therefore, the missing side length of the smaller triangle is 3.5 units.
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