Two sides of a triangle measure 17 inches and 20 inches. Which CANNOT be the length of the remainig side? B
37
A
7
D
20
12

Work Shown:

We have a triangle with sides a,b,c such that

The third side c can be represented by this inequality

b-a < c < b+a

which is a modified form of the triangle inequality theorem.

Plug in the given values to get

b-a < c < b+a

20-17 < c < 20+17

3 < c < 37

The third side length is between 3 and 37; it cannot equal 3, and it cannot equal 37. So we exclude both endpoints.

Of the answer choices, the values {7,20, 12} are in the range 3 < c < 37.

The value c = 37 is not in the range 3 < c < 37 because we can't have the third side equal to either endpoint. Otherwise, we get a straight line instead of a triangle forming.

So that's why 37 is the only possible answer here.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

its a straight line parallel to the time axis