A=-4, b=-1, c=3 and d=4
A triangle has no croquet sides the lengths of two sides of a triangle are an and bd. Use the numbers above to determine the lengths an and bd. Then use the triangle inequality theorem to determine which two segments have lengths that could be used as the third side of the triangle. Select a response containing 2 possiable answers
The options are
Cd and ac
Bc and ad
Ac and bc
Bc and cd
To determine the lengths of an and bd, we substitute the given values into the variables:
a = -4
n = -1
b = -1
d = 4
Therefore, an = (-4)(-1) = 4 and bd = (-1)(4) = -4.
Now, we need to determine which two segments have lengths that could be used as the third side of the triangle. We use the triangle inequality theorem, which states that for a triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Sorting the given lengths in ascending order, we have: -4, -1, 3, 4.
Keeping this in mind, the two segments that could be used as the third side of the triangle are:
1) Bc and Ad: 3 + (-4) > 4 (satisfies the inequality)
2) Bc and Cd: 3 + 4 > -1 (satisfies the inequality)
Therefore, the correct answer is Bc and Ad, and Bc and Cd.