Question

hannah is a farmer who is building a pen for some animals. the first side of the pen is the longest, measuring 21 feet. the second side of the pen is 11 feet long. how long is the third side of the pen? round your answer to two decimal places.

(image of a right triangle with one leg 11 ft, hypotenuse 21 ft, and the other leg (third side) unknown)

show your work here
hint: to add the square root symbol (√), type
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Explanation:

Step1: Identify the triangle type

The pen is a right - triangle, with hypotenuse \( c = 21\) ft and one leg \( a = 11\) ft. We use the Pythagorean theorem \( c^{2}=a^{2}+b^{2}\), so we can solve for the other leg \( b\): \( b=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute the values

Substitute \( c = 21\) and \( a = 11\) into the formula: \( b=\sqrt{21^{2}-11^{2}}=\sqrt{441 - 121}=\sqrt{320}\)

Step3: Calculate the square root

\(\sqrt{320}\approx17.89\) (rounded to two decimal places)

Answer:

The length of the third side of the pen is approximately \(17.89\) feet.