Question

if these two shapes are similar, what is the measure of the missing length k?
4 cm
1 cm
k
3 cm
k = centimeters
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Explanation:

Step1: Set up proportion for similar shapes

Since the two triangles are similar, their corresponding sides are proportional. Let the ratio of the larger triangle to the smaller triangle be based on the vertical sides. The vertical side of the smaller triangle is 1 cm, and the vertical side of the larger triangle is 3 cm. The horizontal side of the smaller triangle is 4 cm, and the horizontal side of the larger triangle is \( k \). So we set up the proportion: \(\frac{k}{4}=\frac{3}{1}\)

Step2: Solve for \( k \)

Cross - multiply the proportion: \( k\times1 = 4\times3 \)
Simplify the right - hand side: \( k = 12 \)

Answer:

\( k = 12 \)