Answer:
To determine the equations that can be used to find the lengths of the legs of the right triangle, we need to identify the correct equation based on the given information. Let's evaluate each option:
0.5(x)(x + 2) = 24:
This equation represents the formula for the area of a triangle, which is half the product of the base and height. However, it does not provide information about the lengths of the legs of the triangle. Therefore, this equation is not suitable for finding the lengths of the legs.
x(x + 2) = 24:
This equation represents the product of the lengths of the legs of the triangle. It can be rewritten as a quadratic equation: x^2 + 2x - 24 = 0. This equation can be used to find the lengths of the legs.
x^2 + 2x - 24 = 0:
This is the quadratic equation derived from the above option. It can be used to find the lengths of the legs.
x^2 + 2x - 48 = 0:
This equation does not correspond to the given area of 24 square feet. Therefore, it cannot be used to find the lengths of the legs.
x^2 + (x + 2)^2 = 100:
This equation does not represent the area of the right triangle. It seems to be a different equation involving the lengths of the legs and the hypotenuse, but it is not applicable to find the lengths of the legs based on the given information.
Based on the evaluation, the three equations that can be used to find the lengths of the legs of the triangle are:
- x(x + 2) = 24
- x^2 + 2x - 24 = 0
- 0.5(x)(x + 2) = 24
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