Answer:
Longer side = 84 meters
Shorter side = 80 meters
Step-by-step explanation:
The hypotenuse is the longest side of the right angle triangle. Let x represent the length of the longer side of the triangle. The difference between the other two sides is 4 meters. It means that the length of the shorter side is x - 4
Applying Pythagoras theorem which is expressed as
Hypotenuse² = longer side² + shorter side²
Therefore,
116² = x² + (x - 4)²
13456 = x² + x² - 4x - 4x + 16
2x² - 8x + 16 - 13456 = 0
2x² - 8x - 13440 = 0
Dividing through by 2, it becomes
x² - 4x - 6720
x² + 80x - 84x - 6720 = 0
x(x + 80) - 84(x + 80) = 0
x - 84 = 0 or x + 80 = 0
x = 84 or x = - 80
Since the length cannot be negative, then
x = 84
Length of shorter side is
84 - 4 = 80
