The longest side of a right triangle is 15 feet. The third side is 15 less than three times the shortest side. Find the length of the shortest side.

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.