A concrete patio area is shaped like a right triangle. The hypotenuse is one foot longer than one of the legs.The other leg is 9 feet. Sketch a diagram and name the unknown sides. Translate to an equation and solve it. Write a conclusion that states the lengths of the missing sides, including the units.

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