Question

a certain polygon has a total of five diagonals that can be drawn from all vertices. how many sides would that polygon have?
select one:
a. 3
b. 7
c. 5
d. 2

a scalene triangle has
select one:
a. no equal sides
b. three equal sides
c. two equal sides

Explanation:

First Question (Polygon Diagonals)

Step1: Recall diagonal count formula

The total number of diagonals $D$ in an $n$-sided polygon is given by:
$$D = \frac{n(n-3)}{2}$$

Step2: Substitute given diagonal count

Set $D=5$, solve for $n$:
$$5 = \frac{n(n-3)}{2}$$

Step3: Rearrange to quadratic equation

Multiply both sides by 2, rearrange terms:
$$n^2 - 3n - 10 = 0$$

Step4: Factor and solve for $n$

Factor the quadratic:
$$(n-5)(n+2)=0$$
Since side count cannot be negative, $n=5$.

A scalene triangle is defined as a triangle where all three sides have different lengths, meaning it has no equal sides. A triangle with three equal sides is equilateral, and one with two equal sides is isosceles.

Answer:

c. 5

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Second Question (Scalene Triangle)