Answer:
24 m, 25 m
Explanation:
You want the two sides of a right triangle that are consecutive integers when one side is 7 m.
Pythagorean theorem
Let the shorter side be represented by x. Then the longer side is x+1, and the Pythagorean theorem tells you ...
7² +x² = (x+1)²
49 +x² = x² +2x +1
48 = 2x . . . . . . subtract (x²+1)
24 = x
x+1 = 25
The other sides are 24 and 25 meters.
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Additional comment
You know that 7 is not the hypotenuse, because a 3-4-5 right triangle is the only right triangle with consecutive integer leg lengths and a hypotenuse of 7 or less. (The next nearest right triangle with consecutive leg lengths is {20, 21, 29}, with a hypotenuse of 29.)
You may recognize the side lengths as the Pythagorean Triple {7, 24, 25}, one of the triples commonly seen in algebra and trig problems.