If two sides of a triangle have lengths of 1/4 and 1/5, which fraction can NOT be the length of the third side?
1/2
Its not a Right Triangle, so i cant use the pythagorean theorem.
Cant the third side be any value?
dsdsaasd
Well, triangles can't have sides with a length of zero, so that rules out any fraction with a denominator of zero. So, don't be a zero and avoid fractions like 1/0! Trust me, you don't want to divide by zero and cause a mathematical catastrophe!
To determine which fraction cannot be the length of the third side of a triangle given that the lengths of two sides are 1/4 and 1/5, we can apply the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for any triangle with sides a, b, and c, the following inequality holds:
a + b > c
a + c > b
b + c > a
Now, let's apply this theorem to our question. We know that two sides have lengths of 1/4 and 1/5. Let's assume that the third side has a length of x, where x is a fraction.
Using the triangle inequality theorem, we can write the following inequalities:
1/4 + 1/5 > x
1/4 + x > 1/5
1/5 + x > 1/4
To simplify these inequalities, we can find a common denominator:
(5+4)/20 > x
(1+4x)/20 > 1/5
(1+5x)/20 > 1/4
Simplifying further:
9/20 > x
(1+4x)/20 > 1/5
(1+5x)/20 > 1/4
Now, we can compare the fractions to determine which is not possible for the length of the third side.
From the first inequality, we see that x must be less than 9/20 for it to be a valid length for the third side.
From the second inequality, we find that x must be greater than (1/5 - 1)/4 or x > -3/20.
From the third inequality, we find that x must be greater than (1/4 -1)/5 or x > -4/25.
Combining these conditions, we find that the fraction x cannot be less than 9/20, greater than -3/20, or greater than -4/25.
Therefore, the fraction that cannot be the length of the third side is 9/20.