An isosceles triangle has a base of 9.8 units long. If the congruent side lengths have measures to the first decimal place, what is the shortest possible length of the sides.
a + c > b,
a + c > 9.8, a - c.
Substitute a for c:
a + a > 9.8,
2a > 9.8,
a > 4.9,
a = c = 5.1.
To find the shortest possible length of the congruent sides of an isosceles triangle, we need to consider the concept of triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In an isosceles triangle, the congruent sides are equal in length. Let's assume the length of each congruent side is "x" units.
Now, applying the triangle inequality theorem, we have:
x + x > 9.8 (Sum of two congruent sides is greater than the base)
2x > 9.8
x > 9.8 / 2
x > 4.9
Therefore, the shortest possible length of the congruent sides is 4.9 units when rounded to the first decimal place.