Question

A triangle has side lengths measuring 3x cm, 7x cm, and h cm. Which expression describes the possible values of h, in cm?
4x < h < 10x
10x < h < 4x
h = 4x
h = 10x

Answer 1

The length of the side of a triangle is greater than the difference of the lengths of the other two sides and less than the sum of the lengths of the other two sides.

Answer 2

I don't understand.

Answer 3

Let's say a triangle has two sides that are 8 and 12.

The third side must be greater than the difference of the other two sides.
The difference of 12 - 8 = 4, so the third side must be grater than 4.

Also, the third side must be less than the sum of the other two sides.
That means the third side must be less than 20, since 8 + 12 = 20.

Answer 4

In other words, when you are given two side of a triangle, find the sum and the difference of those sides.
The third side is between the difference and the sum.

Answer 5

so A?

Answer 6

Now look at your problem.
You know two sides are 3x and 7x, right?

Answer 7

Yes. So it would be more than 4 and less than 10, right?

Answer 8

Yes, you are correct.
Difference: 7x - 3x = 4x
Sum: 3x + 7x = 10x
h must be between 4x and 10x.
That is choice A.
Good job!

Answer 9

Thanks so much!

Answer 10

Notice that choices C and D are incorrect because h must be grater than 4x, not equal to 4x.
h must also be less than 10x, not equal to 10 x.

Answer 11

You're welcome.