The length of the shorter leg is 2.4 ft, and the length of the longer leg is 4.4 ft
<h3>Calculating the lengths of the legs of a right triangle</h3>
From the question, we are to determine the lengths of the legs of the right triangle.
Let the hypotenuse of the right triangle be c and the lengths of the legs be a and b
From the given information,
The hypotenuse of the right triangle is 5 feet long
c = 5
and
One leg is 2 feet longer than the other
Then, we can write that
b = a + 2
From the <em>Pythagorean theorem</em>,
c² = a² + b²
Thus,
5² = a² + (a + 2)²
5² = a² + (a + 2)(a + 2)
25 = a² + a² + 2a + 2a + 4
25 = a² + a² + 4a + 4
25 = 2a² + 4a + 4
2a² + 4a + 4 - 25 = 0
2a² + 4a - 21 = 0
Solving the quadratic equation, we get
a = -4.4 OR a = 2.4
Since, length a cannot be negative, a = 2.4
Substitute the value of a into the equation
b = a + 2
b = 2.4 + 2
b = 4.4
Hence, the lengths of the legs are 2.4 and 4.4
Learn more on Calculating the legs of a right triangle here: brainly.com/question/13944681
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