Question

a 6 - foot - tall scarecrow in a farmers field casts a shadow that is 21 feet long. a dog standing next to the scarecrow is 2 feet tall. since they both make similar triangles, how long is the dogs shadow?
7 ft
63 ft
42 ft
12 ft

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratio of height to shadow length is equal. Let \(x\) be the dog's shadow length. The proportion is \(\frac{6}{21}=\frac{2}{x}\).

Step2: Cross - multiply

Cross - multiply the proportion: \(6x = 2\times21\).

Step3: Solve for \(x\)

First, calculate \(2\times21 = 42\). Then, \(6x=42\), so \(x=\frac{42}{6}=7\).

Answer:

A. 7 ft