Answer:
5 meters
Explanation:
You want to know the width of a rectangular living room that is 12 m along one side and 13 m along the diagonal.
Diagonal
The diagonal of a rectangle is the hypotenuse of each of the right triangles it creates by dividing the rectangle in half. If one side length is 12 and the diagonal is 13, these measures are part of the {5, 12, 13} Pythagorean triple.
The width of the living room is 5 meters.
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Additional comment
You can use the Pythagorean theorem to find the missing length:
13² = 12² +w²
169 -144 = w²
w = √25 = 5
The width of the living room is 5 meters.
Other Pythagorean triples you see in algebra, trig, and geometry problems are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41} and their multiples.