Provide an appropriate response.Maria's teacher asked her to solve the following problem: "One leg of a right triangle is 5 m longer than the other. The length of the hypotenuse is 25 m. Find the lengths of the legs." Maria called the legs x and y and translated the problem into the following equation: 
After that she was unsure of how to proceed. Why is Maria's equation not very useful? Write the correct equation and find the solution to the problem showing all the steps of your work.
What will be an ideal response?
Maria's equation contains two different variables and thus it cannot be solved. By using the information about how the two leg lengths are related, it is possible to obtain an equation containing only one variable.
x2 + (x + 5)2 = 252
x2 + x2 + 10x + 25 = 625
2x2 + 10x + 25 = 625
2x2 + 10x - 600 = 0
2(x2 + 5x - 300) = 0
2(x + 20)(x - 15) = 0
x = -20 or x = 15
A side length cannot be negative, so x = 15 and the leg lengths are 15 m and 20 m.
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