Answer:
x= -4
Step-by-step explanation:
This is correct because no other options fit.
The small & large triangle are similar the we can write the following proportion/ratio:
8/(8+x) = 12/(12+18) ==> 12(8+x) =8(12+18) ==> 96+12x=240
12x =240-96 ==> 12x = 144 and x=12
Step-by-step explanation:
Pythagoras' theorem for the smallest one :
![c^2 = 4^2 + 6^2](https://tex.z-dn.net/?f=c%5E2%20%3D%204%5E2%20%2B%206%5E2)
![c^2 = 16 + 36](https://tex.z-dn.net/?f=c%5E2%20%3D%2016%20%2B%2036)
= 52
Pythagoras' theorem for the middle one :
=
+ ![a^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D)
Pythagoras' theorem for the biggest one :
![(4+a)^2 = c^2 + b^2](https://tex.z-dn.net/?f=%284%2Ba%29%5E2%20%3D%20c%5E2%20%2B%20b%5E2)
![16 + 8a + a^2 = 52 + b^2](https://tex.z-dn.net/?f=16%20%2B%208a%20%2B%20a%5E2%20%3D%2052%20%2B%20b%5E2)
Using the formula before (for
) it becomes :
![16 + 8a + a^2 = 52 + (6^2 + a^2)](https://tex.z-dn.net/?f=16%20%2B%208a%20%2B%20a%5E2%20%3D%2052%20%2B%20%286%5E2%20%2B%20a%5E2%29)
![16 + 8a + a^2 = 52 + 6^2 + a^2](https://tex.z-dn.net/?f=16%20%2B%208a%20%2B%20a%5E2%20%3D%2052%20%2B%206%5E2%20%2B%20a%5E2)
![16 + 8a = 52 + 6^2](https://tex.z-dn.net/?f=16%20%2B%208a%20%3D%2052%20%2B%206%5E2)
16 + 8a = 52 + 36
16+8a = 88
8a = 88-16
8a = 72
a = 9
Verifying :
![b^2 = 6^2 + a^2](https://tex.z-dn.net/?f=b%5E2%20%3D%206%5E2%20%2B%20a%5E2)
![b^2 = 36 + 81](https://tex.z-dn.net/?f=b%5E2%20%3D%2036%20%2B%2081)
![b^2 = 117](https://tex.z-dn.net/?f=b%5E2%20%3D%20117)
= 117
The biggest one :
![(4+a)^2 = c^2 + b^2](https://tex.z-dn.net/?f=%284%2Ba%29%5E2%20%3D%20c%5E2%20%2B%20b%5E2)
![(4+9)^2 = 52 + 117](https://tex.z-dn.net/?f=%284%2B9%29%5E2%20%3D%2052%20%2B%20117)
![13^2 = 169](https://tex.z-dn.net/?f=13%5E2%20%3D%20169)
True
First find the total they both paid, if 15%=$3.90
100%=$26Then, find the total of Max’s lunch M= $26-$14= $12M= 3.90(6.6666) - aWhere a = 14
Answer:
260 feet of fence
Step-by-step explanation:
The area of a triangle is found using the formula A=.5(base)(height). You can plug in your known values to solve for the base of the triangle. (It should look something like 600=.5(40)(x), where you can combine to get 600=20x, divide by 20, and get that x =30.). Next, to find the diagonal length of the triangle, you use the Pythagorean theorem, which is
. You plug in 40 for a, and 30 for b, and solve to get that c is 50. You now have all of your missing side lengths. You add them all together (40+70+70+30+50) to get 260.