Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true? This triangle e
2 answers:
If you have a triangle with sides a, b and c, then:
In your case let a=4 in, b=12 in annd c=17 in. Check these three inequalities:
1. 4+12=16 is less than 17 - inequality a+b>c doesn't hold.
2. 4+17>12 - inequality a+c>b holds.
3. 12+17>4 - inequality b+c>a holds.
Since only two from three inequalities are true, then the triangle doesn't exist.
Answer: correct choice is D - This triangle does not exist because the sum of 4 and 12 is less than 17.
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Remember that the radicand (the area under the root sign) must be positive or zero for a radical with an even index (like the square root or fourth root, for example). This is because two numbers squared or to the fourth power, etc. cannot be negative, so there are no real solutions when the radicand is negative. We must restrict the domain of the square-root function.
If the domain has already been restricted to
, we can work backwards to add 11 to both sides. We see that 
must be under the radicand, so the answer is A.
If the domain has already been restricted to