- The sketch is given by the image at the end of this answer.
- Applying the Pythagorean Theorem, it is found that the length of the other leg is of 40 feet and the length of the hypotenuse is of 41 feet.
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In a right triangle, the legs [tex]l_1[/tex] and [tex]l_2[/tex] are related with the hypotenuse [tex]h[/tex] by the Pythagorean Theorem, given below:
[tex]h^2 = l_1^2 + l_2^2[/tex]
In this problem:
- One of the legs is 9 feet, thus [tex]l_1 = 9[/tex]
- The hypotenuse is 1 feet longer than the other leg, thus [tex]l_2 = x, h = x + 1[/tex]
Applying the Pythagorean Theorem:
[tex]h^2 = l_1^2 + l_2^2[/tex]
[tex]9^2 + x^2 = (x + 1)^2[/tex]
[tex]81 + x^2 = x^2 + 2x + 1[/tex]
[tex]2x + 1 = 81[/tex]
[tex]2x = 80[/tex]
[tex]x = \frac{80}{2}[/tex]
[tex]x = 40[/tex]
- Applying the Pythagorean Theorem, it is found that the length of the other leg is of 40 feet and the length of the hypotenuse is of 41 feet.
A similar problem is given at https://brainly.com/question/21691542
