<span> When area is equal 1120. We can write an equation
(x+4)(-x+64)=1120
-x²-4x+64x+256=1120
-x²+60x+256-1120=0
-x²+60x-864=0
D=b² - 4ac= 3600-4*864=144, √D=12
x= (-b+/-√D)/2a
x=(-60+/-12)/(-2)
x=24, x=36
For x=24
(x+4)=24+4=28
(-x+64)=(-24+64)=40
For x=36
(x+4)=36+4=40
(x-64) =(-36+64)=28
So sides should be 28 and 40 in.
We did not get any extraneous solutions. They could be if we get negative length side, for example. They can come because a quadratic equation can
give positive and negative numbers because a^2 and (-a)^2 give the same positive number.
We chose to solve this equation using formula for quadratic equations, because this equation has too big numbers to solve it using other methods.
</span>
12.5 x 4... hope this helped!
Answer:
The length of apothem of given hexagon is 8.66 cm
Step-by-step explanation:
Apothem of a polygon is given by:
![apothem = \frac{s}{2\ tan\ (\frac{180}{n})}](https://tex.z-dn.net/?f=apothem%20%3D%20%5Cfrac%7Bs%7D%7B2%5C%20tan%5C%20%28%5Cfrac%7B180%7D%7Bn%7D%29%7D)
Here
s is length of side
tan is trigonometric function
and n denotes number of sides
Given that the polygon is a hexagon
![s = 10cm\\n = 6](https://tex.z-dn.net/?f=s%20%3D%2010cm%5C%5Cn%20%3D%206)
Putting the values in the formula
![apothem = \frac{10}{2\ tan\ (\frac{180}{6})}\\= \frac{10}{2\ tan\ 30}\\=\frac{10}{2 * 0.5773}\\=\frac{10}{1.1546}\\=8.6610\\Rounding\ off\ to\ nearest\ hundredth\\= 8.66\ cm](https://tex.z-dn.net/?f=apothem%20%3D%20%5Cfrac%7B10%7D%7B2%5C%20tan%5C%20%28%5Cfrac%7B180%7D%7B6%7D%29%7D%5C%5C%3D%20%5Cfrac%7B10%7D%7B2%5C%20tan%5C%2030%7D%5C%5C%3D%5Cfrac%7B10%7D%7B2%20%2A%200.5773%7D%5C%5C%3D%5Cfrac%7B10%7D%7B1.1546%7D%5C%5C%3D8.6610%5C%5CRounding%5C%20off%5C%20to%5C%20nearest%5C%20hundredth%5C%5C%3D%208.66%5C%20cm)
Hence,
The length of apothem of given hexagon is 8.66 cm
Answer:
5
Step-by-step explanation:
Cause I'm smart