An isosceles triangle has a base 9.2 units long. if the congruent side lengths have measures to the first decimal place, what is the shortest possible length of the sides?

Question:

An isosceles triangle has a base of 9.6 units long. If the congruent side lengths have measures to the first decimal place, what is the possible length of the sides? 9.7, 4.9, or 4.7

4.9 is the shortest possible length of the sides.

Step-by-step explanation:

Given:

The base of the triangle base  =   9.2 units

To Find:

The shortest possible length of the sides = ?

Solution:

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

So According to the theorem

In the given option 4.9 is the shortest length greater than 4.8 that can be possible.

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.