In triangle ABC, the length of side AB is 19 inches and the length of side BC is 28 inches. Which of the following could be the length of side AC? A.
52 inches
B.
7 inches
C.
42 inches
D.
49 inches

Explanation:

Let's say we have a triangle with sides x,y,z

Also, let's further say we know that x = 19 and y = 28 (from AB and BC respectively).

The third missing side z can't be nailed down to a single number, but we can establish a possible range. That range is

y-x < z < y+x

28-19 < z < 28+19

9 < z < 47

So any number between 9 and 47, excluding both endpoints, will work as a possible side length for the third missing side.

Something like 7 inches is too small, so we rule out choice B. Choice D is ruled out since 49 inches is too big. Same goes for choice A also.

The only thing left is choice C. The 42 is between 9 and 47

In other words, 9 < 42 < 47 is true.

So that's why the third missing side could be 42 inches.

Side note: I'm using a modification of the triangle inequality theorem.

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step-by-step explanation:

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.