Answer:
The correct option is (D) 7 inches.
Step-by-step explanation: Given that the lengths of two sides of a triangle are 10 inches and 4 inches.
We are to select the correct dimension that the third side of the triangle may be.
We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
If the third dimension is 4 inches, then we have
10+4 > 4,~~4+10 > 4,~~4+4 < 10.10+4>4, 4+10>4, 4+4<10.
So, this option is not correct.
If the third dimension is 5 inches, then we have
10+4 > 5,~~5+10 > 4,~~5+4 < 10.10+4>5, 5+10>4, 5+4<10.
So, this option is not correct.
If the third dimension is 6 inches, then we have
10+4 > 6,~~6+10 > 4,~~6+4=10.10+4>6, 6+10>4, 6+4=10.
So, this option is not correct.
If the third dimension is 7 inches, then we have
10+4 > 7,~~7+10 > 4,~~7+4 > 10.10+4>7, 7+10>4, 7+4>10.
So, this option is correct, because the sum of the lengths of any two sides is greater than the length of the third side.
Thus, the correct option is (D) 7 inches.
Explanation:
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