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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

User RyPeck
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1 Answer

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we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

Three conditions mus be satisfied

Condition N
1


3x+7x > h\\ 10x > h\\h< 10x

Condition N
2


3x+h > 7x\\ h > 7x-3x\\h> 4x

Condition N
3


7x+h > 3x\\ h > 3x-7x\\h> -4x (condition N 3 is included in condition N 2)

therefore


h> 4x\\ h< 10x\\ 4x < h < 10x

the answer is the option

4x < h < 10x



User Moshfiqur
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