Question

if these two shapes are similar, what is the measure of the missing length x?
8 in
2 in
4 in
x
x = inches
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Explanation:

Step1: Recall similar figures property

For similar shapes, corresponding sides are proportional. So, \(\frac{\text{Side of larger triangle}}{\text{Side of smaller triangle}}=\frac{\text{Corresponding side of larger triangle}}{\text{Corresponding side of smaller triangle}}\)

Step2: Identify corresponding sides

Larger triangle has sides 8 in (corresponding to 4 in of smaller) and 2 in (corresponding to \(x\) of smaller). Set up proportion: \(\frac{8}{4}=\frac{2}{x}\)

Step3: Solve for \(x\)

Cross - multiply: \(8x = 4\times2\) → \(8x = 8\) → \(x=\frac{8}{8}=1\)

Answer:

1