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Question

State whether following statement is true or false.
Two sides of a triangle have lengths 7 inches and 10 inches, as shown. The length of third side must be greater than 3 inches but less than 17 inches long.
1309516_c4da92aab72149c089aa40a4442b8bf9.png

A
True
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B
False
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Solution

The correct option is A True
By applying the triangle inequality,
7<x+10,10<x+7 and x<10+7
We solve each of these inequalities to find
3<x,3<x, and x<17
As x must be positive, thus, from the given inequalities third side must be greater than 3 inches but less than 17 inches long.

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