Question

Use the diagram below to answer questions 1-6. All rooms are rectangular. 1. What is the value of side A? Explain your thinking. 2. What is the value of side B? Explain your thinking. 3. What is the value of side c? Explain your thinking. 4. What is the area of the vegetable garden? Show your thinking

Answer 1

1. The answer is A = x since the opposite sides of a rectangle are the same length.
2. We'll have B = 9x+2 since this must add to x+4 to result in 10x+6. You could also do (10x+6) - (x+4) and you'll end up with 9x+2.
3. On the far left side, (5x-3)+A = 5x-3+x = 6x-3. The far right side must add to this. So, x+C+x-2 = 6x-3 turns into C = 4x-1 after isolating C.
4. Multiply out (5x-3) with (9x+2) to get the full area of 45x^2-17x-6. The steps are shown below

(5x-3)(9x+2)

5x(9x+2)-3(9x+2)

45x^2+10x-27x-6

45x^2-17x-6

You could also use the FOIL rule to get this answer. The box method is another alternative.