Quadratic formula help .

In summary, to fence a rectangular plot of land alongside a lake, with 100m of fencing, and an area of 500m^2, the dimensions of the plot of land should be 44.3m by 11.4m or 5.6m by 88.8m. This is found by solving the perimeter and area formulas and using the quadratic formula to find the values for x and y.
  • #1
travishillier
15
0
Quadratic formula help ...

Heres the question ... your help is greatly needed and appreciated ...

Markita wants to fence a rectangular plot of land along side the shore of a lake. Only 3 sides must be fenced, since the lake will form teh lake will form teh fourth side. Markita had 100m of fencing, and she wants the plot of land to have an area of 500m^2 (squared). Find teh dimensions of the plot of land, to the nearest tenth of a metre. Expalin and justify your solution.


Theres thequestion , lmk what u can do to help me out ... Thx
 
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  • #2
Please don't post the same topic twice...

cookiemonster
 
  • #3
srry won't happen again .. thx
 
  • #4
Well, here's your formulas.

P: 100 = 2x + y [normally, perimeter would be 2x + 2y, but because one of the sides is the lake, you don't count one of the y's]
A: 500 = x*y

Now, solve the first equation for y...

y = 100 - 2x

And substitute it into the area formula...

500 = x(100 - 2x)
500 = 100x - 2x^2
2x^2 - 100x + 500 = 0

Now, you can take the above and put it into the quadratic formula...

[-b +/- sqrt(b^2-4ac)]/2a
a = 2
b = -100
c = 500

Substituting in, you get 44.3 and 5.6 as the two solutions. Now, that's x...now we need y...go back to the perimeter formula...

y = 100 - 2x

Substituting in the two numbers we found above for x, you get...

Solution 1: x = 44.3, y = 11.4
Solution 2: x = 5.6, y = 88.8

If you multiply them to check the area, you'll get around 497 and 505, which isn't exactly 500, but you were asked to give rounded values to the nearest tenth, so that's okay.
 

1. What is the quadratic formula?

The quadratic formula is a mathematical equation used to solve quadratic equations, which are equations in the form of ax^2 + bx + c = 0. It is written as x = (-b ± √(b^2-4ac)) / 2a.

2. When is the quadratic formula used?

The quadratic formula is used when solving quadratic equations, which can arise in many different fields such as physics, engineering, and economics.

3. How do I use the quadratic formula?

To use the quadratic formula, first identify the values of a, b, and c in the equation ax^2 + bx + c = 0. Then, plug these values into the formula and solve for x. There may be two solutions, as indicated by the ± symbol.

4. What are the advantages of using the quadratic formula?

The quadratic formula is a reliable and accurate method for solving quadratic equations. It can be used to find solutions for any quadratic equation, regardless of the values of a, b, and c. It is also a useful tool for graphing quadratic functions.

5. Are there any alternatives to using the quadratic formula?

Yes, there are other methods for solving quadratic equations, such as factoring and completing the square. However, the quadratic formula is often the most efficient and straightforward method, especially for complex equations.

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