The lengths of the sides of a rectangle are a and b…

The lengths of the sides of a rectangle are a and b, where a > b The sum of the lengths of the two shorter sides and one of the longer sides of the rectangle is 36. What value of a maximizes the area of the rectangle?

A .9
B. 12
C. 18
D. 24

The answer is C. I suspect there is an easier way to solve than completing the square and finding the vertex of the resulting quadratic function. What is your most direct, easy to understand solution to this calculator-allowed question?

In question #10 of the backsolving chapter…

In question #10 of the backsolving chapter : in the xy plane, a line containing the points (a, a^3) and (10,40) passes through the origin. Which of the following could be the value of a?

I found the explanation in the answer key to be too time-consuming if I were to solve the equation with backsolving. Can you explain how to solve this question algebraically instead?

Test 7 Section 4 Question 6

Hi Mike…SAT 7, Section 4, Q6: I now see the shortcut here (that both sides of the equation are perfect squares,) but if I did expand and FOIL the left side, wouldn’t I still get the correct “a” values even though it takes longer? I can’t get it to work !! Can you please show the alternate path math steps? Or is recognizing the perfect squares the ONLY way to solve this one ? Thanks!

SAT 8, Section 3, Number 7

Hi Mike, I’m asking about SAT 8, Section 3, Number 7. Is it always best to immediately plug in answer choices on questions like this? For the algebraic practice, I rewrote the equation as a quadratic and solved for (x=5) and (x= -1). Then sub’d each value back into the given equation to find that only (x=5) worked. OK…but what a time-killer at #7 out of 20. Any other solution path to consider? Thanks!