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

Answer with explanation:

In a triangle sum of two sides , should always be greater than the third side.

Sides of the given triangle are, 3 x cm, 7 x cm and h cm.

1.

3 x + 7 x > h

→ 10 x > h

2.

3 x+ h > 7 x

→h > 7 x -3 x

→h> 4 x

3.

7 x + h > 3 x, which will be always true.

Combining 1, 2 and 3 we get

→4 x < h < 10 x

Option A

Answer 2

Since it the measurements of the other sides are already given, the value that we are going to find would be the height. 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. So given that the two lengths are 3x cm and 7x cm, the height should be more than 4x but less than 10x. Therefore, the answer is the first option: 4x < h < 10x.