Answer:
Part 1) ![42=\frac{1}{2}x(x-5)](https://tex.z-dn.net/?f=42%3D%5Cfrac%7B1%7D%7B2%7Dx%28x-5%29)
Part 2) The length of the base is ![x=12\ m](https://tex.z-dn.net/?f=x%3D12%5C%20m)
Step-by-step explanation:
Part 1) Which equation would be help solve the following problem?
Let
x----> the length of the base of a triangle
y----> the height of a triangle
we know that
The area of a triangle is
![A=\frac{1}{2}xy](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dxy)
![A=42\ m^{2}](https://tex.z-dn.net/?f=A%3D42%5C%20m%5E%7B2%7D)
so
------> equation A
-----> equation B
Substitute equation B in equation A
![42=\frac{1}{2}x(x-5)](https://tex.z-dn.net/?f=42%3D%5Cfrac%7B1%7D%7B2%7Dx%28x-5%29)
Part 2) Find the length of the base
we have
![42=\frac{1}{2}x(x-5)](https://tex.z-dn.net/?f=42%3D%5Cfrac%7B1%7D%7B2%7Dx%28x-5%29)
solve for x
![84=x^{2}-5x\\x^{2}-5x-84=0](https://tex.z-dn.net/?f=84%3Dx%5E%7B2%7D-5x%5C%5Cx%5E%7B2%7D-5x-84%3D0)
Solve the quadratic equation by graphing
The solution is ![x=12\ m](https://tex.z-dn.net/?f=x%3D12%5C%20m)
see the attached figure
For this case we have that by definition, the area of a rectangle is given by:
![A = w * l](https://tex.z-dn.net/?f=A%20%3D%20w%20%2A%20l)
Where:
w: Is the width of the rectangle
l: is the length of the rectangle
Each of the girls has 24 feet of fencing, that is, the perimeter is ![P = 2w + 2l = 24.](https://tex.z-dn.net/?f=P%20%3D%202w%20%2B%202l%20%3D%2024.)
Amy:
![l = 6 \ ft\\2w + 2 (l) = 24\\2w + 2 (6) = 24\\2w + 12 = 24\\2w = 24-12\\2w = 12\\w = 6](https://tex.z-dn.net/?f=l%20%3D%206%20%5C%20ft%5C%5C2w%20%2B%202%20%28l%29%20%3D%2024%5C%5C2w%20%2B%202%20%286%29%20%3D%2024%5C%5C2w%20%2B%2012%20%3D%2024%5C%5C2w%20%3D%2024-12%5C%5C2w%20%3D%2012%5C%5Cw%20%3D%206)
Thus, Amy's fence area is: ![A = 6 * 6 = 36 \ ft ^ 2](https://tex.z-dn.net/?f=A%20%3D%206%20%2A%206%20%3D%2036%20%5C%20ft%20%5E%202)
Zach:
![l = 8 \ ft\\2w + 2l = 24\\2w + 2 (8) = 24\\2w + 16 = 24\\2w = 24-16\\2w = 8\\w = 4](https://tex.z-dn.net/?f=l%20%3D%208%20%5C%20ft%5C%5C2w%20%2B%202l%20%3D%2024%5C%5C2w%20%2B%202%20%288%29%20%3D%2024%5C%5C2w%20%2B%2016%20%3D%2024%5C%5C2w%20%3D%2024-16%5C%5C2w%20%3D%208%5C%5Cw%20%3D%204)
Thus, the area of Zach's fence is:![A = 4 * 8 = 32 \ ft ^ 2](https://tex.z-dn.net/?f=A%20%3D%204%20%2A%208%20%3D%2032%20%5C%20ft%20%5E%202)
Answer:
Amy's garden has a greater area
, is
greater
Answer:
20 inches
Step-by-step explanation:
x/2=10
20/2=10
Answer:
it really depends on your previous test marks.
if you have scored well in previous tests there are chances you won't get bad grades in your report card.
best of luck