Solve the applied problem.One corner of an 8.5 × 11 inch piece of paper is folded over to...

Solve the applied problem.

One corner of an 8.5 × 11 inch piece of paper is folded over to the opposite side, as shown in the figure. The area of the darkly shaded triangle at the lower left of the figure is 6 square inches and we want to find the length x.

(a) Take a piece of paper this size and experiment. Approximately, what is the largest value x could have (and still have the paper look like the figure)? With this value of x, what is the approximate area of the triangle? Try some other possibilities.

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(b) Now find an exact answer by constructing and solving a suitable equation. Explain why one of the solutions to the equation is not an answer to this problem.