Question

if these two shapes are similar, what is the measure of the missing length k? 40 mm 15 mm 12 mm k = millimeters

Explanation:

Step1: Set up proportion

For similar - shaped triangles, the ratios of corresponding sides are equal. Let the ratio of the first pair of corresponding sides be equal to the ratio of the second pair of corresponding sides. So, $\frac{15}{12}=\frac{40}{k}$.

Step2: Cross - multiply

Cross - multiplying gives us $15k = 12\times40$.

Step3: Simplify the right - hand side

$12\times40 = 480$, so $15k=480$.

Step4: Solve for k

Divide both sides of the equation by 15: $k=\frac{480}{15}=32$.

Answer:

32