Acertain right triangle has area 30 in. squared . one leg of the triangle measures 1 in. less than the hypotenuse. let x represent the length of the hypotenuse. a) express the length of the leg mentioned above in terms of x. give the domain of x. b) express the length of the other leg in terms of x. c) write an equation based on the information determined thus far. square both sides and then write the equation with one side as a polynomial with integer coefficients, in descending powers, and the other side equal to 0. divide out any common factors to find the most simplified form. d) solve the equation in part (c) graphically. find the lengths of the three sides of the triangle.

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.