Answer: B P= [tex]\frac{33}{2}[/tex] + [tex]\frac{11}{2}\sqrt{3}[/tex]
Step-by-step explanation:
Given:
h=11
30-60-90 triangle
Find:
Perimeter - all the sides added up
Rules:
In a 30-60-90 triangle, the ratio for a the sides are as follows:
Short leg, across from 30 = x
long leg across from 60 = x√3
hypotenuse, acrosss from 90 = 2x
If h=11, from the rules above
h=2x >substitute h=11
11 = 2x >divide both sides by 2
x = 11/2
short leg = x >from rules
short leg = x/2
long leg = x√3 >from rules
long leg = [tex]\frac{11}{2}\sqrt{3}[/tex]
Perimeter = h +short leg + long leg
Perimeter = 11 + [tex]\frac{11}{2}[/tex] + [tex]\frac{11}{2}\sqrt{3}[/tex]
Perimeter = [tex]\frac{33}{2}[/tex] + [tex]\frac{11}{2}\sqrt{3}[/tex]
B
Answer:
[tex]\textsf{B.} \quad \dfrac{33}{2}+\dfrac{11}{2}\sqrt{3}[/tex]
Step-by-step explanation:
A 30-60-90 triangle is a special right triangle where the measures of its angles are 30°, 60°, and 90°.
In a 30-60-90 triangle, the lengths of its sides are in the ratio 1 : √3 : 2.
Therefore, the formula for the ratio of the sides is x : x√3 : 2x where:
If the hypotenuse of the triangle is 11 units, then 2x = 11.
Solving for x:
[tex]\implies \dfrac{2x}{2} = \dfrac{11}{2}[/tex]
[tex]\implies x=\dfrac{11}{2}[/tex]
As the side opposite the 30° angle is equal to x, then the length of this side is 11/2 units.
This means that the side opposite the 60° angle is:
[tex]\implies x\sqrt{3}=\dfrac{11}{2}\sqrt{3}[/tex]
The perimeter of a two-dimensional shape is the sum of the lengths of all the sides of the shape. Therefore, the perimeter of the 30-60-90 triangle is:
[tex]\begin{aligned}\textsf{Perimeter}&=11+\dfrac{11}{2}+\dfrac{11}{2}\sqrt{3}\\\\&=\dfrac{22}{2}+\dfrac{11}{2}+\dfrac{11}{2}\sqrt{3}\\\\&=\dfrac{22+11}{2}+\dfrac{11}{2}\sqrt{3}\\\\&=\dfrac{33}{2}+\dfrac{11}{2}\sqrt{3}\end{aligned}[/tex]
Learn more about 30-60-90 triangles here:
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