Ace the Officer Aptitude Rating (OAR) 2026 – Unleash Your Inner Officer!

To find the height of the barn using the similarity of triangles, we can set up a proportion based on the corresponding heights and shadow lengths of the farmer and the barn.

The concept of similar triangles tells us that the ratio of the height of an object to the length of its shadow will be the same for both the farmer and the barn. In this scenario, we know that the farmer is 6 feet tall and has a shadow that measures 14 feet. The barn casts a shadow that is 70 feet long, and we need to determine its height.

We can set up the following proportion based on the heights and shadow lengths:

\[

\frac{\text{Height of Farmer}}{\text{Length of Farmer's Shadow}} = \frac{\text{Height of Barn}}{\text{Length of Barn's Shadow}}

\]

Plugging in the known values:

\[

\frac{6 \text{ feet}}{14 \text{ feet}} = \frac{h}{70 \text{ feet}}

\]

To solve for the height of the barn (h), we can cross-multiply:

\[

6 \times 70 = 14 \times h

\]

This simplifies to:

\[

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