Caution
I just finished doing this exact same problem. In nearly 4000 answers, I don't think that's ever happened. It's a great problem. Study it carefully but make sure you handle with care. Most area questions don't work this way.
Remark:
This problem will puzzle you greatly until you look at the diagram carefully.
Draw the diagram so that AC is on the horizontal and make it the longest line. This problem does not require that you have an accurate diagram.
Eyeball P so that it looks like it divides AC in such a way that PC is 2 units and AP is about 3 units. From B draw a line that is Perpendicular to AC. It shouldn't meet P otherwise you will get confused. Where the line from B hits AC label that point D. BD is perpendicular to AC.
What you need to know
BD is the height of both triangles. What does that mean? In practical terms it means that you can call the ratio of the areas 3/2
Ratio
Triangle ABP: Triangle BPC = x/14
3:2 = x:14 Change to a proportion
3/2 = x/14 Cross multiply
3*14 = 2x Combine
42 = 2x Divide by 2
42/2 = x Divide
21 = x
Conclusion One
The area of ABP = 21 square units.
Conclusion Two
Area ABC = Area ABP + Area CBP
Area ABC = 21 + 14 = 35
Nice problem. Be careful how you treat it. Usually these kind of ratio problems don't work this way.
Answer:
B: Each runner varies with respect to multiple variables. Each runner should use both models to account for their individual differences. This will provide an accurate comparison for the difference in wear between the models.
Step-by-step explanation:
Since the shoe company wants to test the wear of the shoes after two months, it means that option B will be the most accurate.
This because everybody has peculiarities in the bodies and also running patterns. These could have an effect on either of their legs. Thus, having to wear a new one on one leg and the original one on another leg for a month and then replacing with the second leg of both for the other month would be the best way to know the true effect of wear on the shoes because they have both been subject to same conditions within exactly the same timeframe.
6 + 7 = 13 - 7 = 6 or 13 - 6 = 7
<span>p=<span><span>2l</span>+<span>2w</span></span></span>Step 1: Flip the equation.<span><span><span>2l</span>+<span>2w</span></span>=p</span>Step 2: Add -2w to both sides.<span><span><span><span>2l</span>+<span>2w</span></span>+<span>−<span>2w</span></span></span>=<span>p+<span>−<span>2w</span></span></span></span><span><span>2l</span>=<span>p−<span>2w</span></span></span>Step 3: Divide both sides by 2.<span><span><span><span><span>2l</span>2</span></span></span>=<span><span><span><span>p−<span>2w</span></span>2</span></span></span></span><span>l=<span><span><span><span>12</span></span>p</span>−<span>w</span></span></span>
