Answer:
The lengths of the two sides are 24 ft and 7 ft.
Step-by-step explanation:
Let's use Pythagorean Theorem to solve this question. Pythagoream Theorem states that a² + b² = c² and is a famous formula used to find the lengths of the sides of a right triangle.
Because we have two unknowns, we will need to set up a system of equations. Let a represent the longer triangle leg and b represent the shorter triangle leg. We can use Pythagorean Theorem to get the first equation, a² + b² = 25².
The second equation can be derived from the first sentence. The short leg is 17 ft shorter than the long leg; this can be represented as b = a - 17.
We can now use substitution to solve for our variables. Substitution is a method of solving systems of equations where one variable is replaced by an equivalent expression. We can replace b with the expression (a-17) in the first equation and solve for a.
a² + (a - 17)² = 625
a² + a² - 34a + 289 = 625
2a² - 34s - 336 = 0
a = -7, 24
The length of a line cannot be negative, so the length of the longer side must be 24 ft. This gives us 7 ft as the length of the shorter side.
Let's plug these values into Pythagorean Theorem equation to check our answer.
24² + 7² = 25²
576 + 49 = 625