Respuesta :
The lengths of the legs of the right triangle are 7 and 24. That is,
7, 24
Calculating the length of the leg of a right triangle
From the question, we are to calculate the length of each leg of the right triangle
From the given information,
Hypotenuse of the right triangle = 25 feet
The length of one leg of the triangle is 10 feet more than twice the other leg
Let the length of the other leg be x
Then,
Length of one of the legs = 10 + 2x
Using the Pythagorean theorem, we can write that
(10 + 2x)² + x² = 25²
(10 + 2x)(10 + 2x) + x² = 625
100 + 20x + 20x + 4x² + x² = 625
100 + 40x + 5x² = 625
5x² + 40x = 625 - 100
5x² + 40x = 525
Divide through by 5
x² + 8x = 105
x² + 8x - 105 = 0
Solve quadratically
x² +15x -7x - 105 = 0
x(x + 15) -7(x + 15) = 0
(x -7)(x + 15) = 0
x - 7 = 0 OR x + 15 = 0
x = 7 OR x = -15
Since x cannot be negative, the value of x is 7
Recall,
The length of one of the legs = 10 + 2x
= 10 + 2(7)
= 10 + 14
= 24
Hence, the lengths of the legs of the right triangle are 7 and 24. That is, 7, 24
Learn more on Calculating the legs of a right triangle here: https://brainly.com/question/917409
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