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Fun with Quadratics and Triangles: Analyzing Routes and Equations

Join Angie and Jordan as they navigate routes, using triangles and quadratics. Discover shortcuts, solve equations, and find areas of shaded regions.

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Fun with Quadratics and Triangles: Analyzing Routes and Equations

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  1. Week 2 Fun With Quadratics and Triangles

  2. Let’s begin with the first triangle. • After Angie and Jordan walked the 3.5 miles to get the waterfall, they realize it would take too long to walk back the same miles to get to the car. • Looking for a shortcut back to the car, Angie found a route that was 2.6 miles long. This shortcut lead straight back to the beginning of the trail and the car. • By taking this route, Angie and Jordan shaved less than 2 minutes off than taking the 8 minute trail back to the car.

  3. Onward to the second triangle. • After looking at the problem, I found out that the short leg is 10, the long leg is 40, and the hypotenuse is 50. How? If I plug in 10 to the formula I came up, which is 20+2a=b, the numbers fit oveall.

  4. Let’s move on to the last problem. • From first glance, I saw that I have to FOIL. After foiling, I get two quadratic equation; x^2+6x+5 and x^2+12x+27. I tried the quadratic formula, but that route only gave me the zeros for both. So, I subtracted the equations from each other. I got 6x+22. Making my new found equation equal 0, I came up with the solution of 3. Plugging 3 into the new equation, i found that the answer is 40. So the area of the blue shaded region is 40.

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