1. Suppose that a certain right triangle PQR with base PR and right angle at R, initially has height which is 2m greater than the base width w.

(i) Sketch the triangle. Be sure to label points P, Q, and R, as well as the lengths of base and height in terms of w.

(ii) Next, suppose this triangle drinks a magic potion and grows 4m taller, while the base stays the same. Sketch this triangle, using the same labeling scheme as in (i).

(iii) Suppose the triangle in (ii) has area 56m2. Write an equation you can solve for w. Do whatever it takes to be sure it has integer coefficients, and set equal to zero.

(iv) Now solve (iii) by factoring. Discuss for each root w of your equation, whether it gives a valid solution for this problem.

(v) So what was the area of the "taller" triangle? Show work, and then answer in a complete sentence that includes the UNITS of your calculation.

(vi) Finally, what were the dimensions of the original triangle? And what was its area? Again show all work, and then answer in a complete sentence that includes the UNITS of base, height, and area.

2. In electronics, if we built a circuit that has two resistors rated U ohms and V ohms set up in a parallel configuration, their equivalent resistance R ohms is given by the formula:

1/R= 1/U+1/V

(i) Suppose you build a circuit whose components have resistances U=3 and V=7 ohms, respectively.

(a) Write the equation given by the data.

(b) Now rewrite (a) so that all three terms have a common denominator.

(c) Now equate the numerators in (b) and find R, the equivalent resistance.

(d) State your solution to (c), in a complete sentence that includes UNITS.

(ii) Next, suppose that in this circuit, U = x-2 and V = x +2 ohms, respectively.

(a) Again, first write the equation you would need to solve to find R. (b) As in (i), rewrite your expression so that there is a common denominator.

(c) Now equate numerators to write an equation you can solve to find R in terms of x. Then find R.

(d) In a complete sentence that includes UNITS, explain the value of R in terms of the variable x.

(e) Finally, comparing (i) with (ii), what would have been the value of x in (i)? And does your answer there agree with your answer in (ii)? Explain in a complete sentence