Questions: Find the distance, d, across the river. Assume that the triangles are similar and the ratio of d to 125 ft is the same as the ratio of 40 ft to 20 ft. The distance across the river is feet.

Find the distance, d, across the river. Assume that the triangles are similar and the ratio of d to 125 ft is the same as the ratio of 40 ft to 20 ft.

The distance across the river is feet.

Transcript text: Find the distance, d, across the river. Assume that the triangles are similar and the ratio of $d$ to 125 ft is the same as the ratio of 40 ft to 20 ft . The distance across the river is $\square$ feet.

Solution

Solution Steps

Step 1: Identify the given ratios

The problem states that the ratio of $ d $ to 125 ft is the same as the ratio of 40 ft to 20 ft. This can be written as: \[ \frac{d}{125} = \frac{40}{20} \]

Step 2: Simplify the known ratio

Simplify the ratio $\frac{40}{20}$: \[ \frac{40}{20} = 2 \]

Step 3: Set up the proportion

Using the simplified ratio, set up the proportion: \[ \frac{d}{125} = 2 \]

Step 4: Solve for $ d $

To find $ d $, multiply both sides of the equation by 125: \[ d = 2 \times 125 \] \[ d = 250 \]