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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.

Sagot :

  • 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

View image Joaobezerra
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