The roof has a base of 24 feet and is slanted at a length of 26 feet. How high is the roof (the vertical height)? Also, calculate the cost of the structure holding up the height if it costs $⁢25 per foot.

The roof’s base, vertical height, and slanted side form a right triangle, with the 26-foot slant as the hypotenuse. By the Pythagorean theorem, the height is √(26² − 24²) = √100 = 10 feet. At $25 per foot, the supporting structure costs 10 × $25 = $250, so the correct choice is “The height is 10 feet, and the cost is 250 dollars.”

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