Answer:
7 m, 24 m, 25 m
Explanation:
This problem can be solved by writing an equation expressing the given relationships and the Pythagorean theorem. Or, it can be solved by reference to common Pythagorean triples. Here, we're interested in a triple that has a difference of 1 between the hypotenuse and the longer leg. Such triples include:
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {9, 40, 41}, {11, 60, 61}, ...
We note that for the triple {7, 24, 25}, the longer leg is 3 more than 3 times the shorter leg: 3 +3(7) = 24.
The side lengths are:
- shorter leg: 7 m
- longer leg: 24 m
- hypotenuse: 25 m
__
In case you're unfamiliar with Pythagorean triples, or you want to write the equation, you can let s represent the length of the shorter side. Then the longer side is (3s+3) and the hypotenuse is (3s+4). The Pythagorean theorem tells you the relation is ...
(3s +4)² = (3s +3)² +s²
9s² +24s +16 = 9s² +18s +9 +s²
s² -6s -7 = 0 . . . . . subtract the left side and put in standard form
(s -7)(s +1) = 0 . . . . factor
s = 7 or -1 . . . . . . solutions to the equation
The side length must be positive, so the shorter leg is 7 meters long. Then the other two legs are ...
3s +3 = 3(7) +3 = 24 . . . . meters
3s +4 = 3(7) +4 = 25 . . . . meters
The side lengths are 7 m, 24 m, and 25 m.