Answer: The shortest side is 9ft
Step-by-step explanation: If the longest side is identified as 15 ft, then we already have our hypotenuse (the longest side in a right angled triangle).
If the shortest side is labelled as x, then the third side of the triangle would be labelled as 3x - 15 (15 less than three times the shortest side).
Now we have three sides of a triangle which we can label as 15, x and 3x - 15
By applying the Pythagoras theorem, AC² = AB² + BC²
(Where AC is the hypotenuse and AB and BC are the other two sides)
15² = X² + (3x-15)²
By expansion, (3x-15)² becomes 9x² - 90x + 225
Hence, 225 = X² + 9X² - 90X + 225
225 = 10X² - 90X + 225
Subtract 225 from both sides of the equation
10X² - 90X = 0
Factorize the left hand side of the equation by 10x
10x (x - 9)= 0
Therefore, either
10x = 0 OR
x - 9 = 0
If 10x=0, then x=0. OR
If x - 9 = 0, then x = 9
The length of the shortest side is 9ft.
