1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
shutvik [7]
3 years ago
13

An equilateral triangle has a side length of 6. What is the height of the triangle?

Mathematics
2 answers:
vlabodo [156]3 years ago
5 0
Since the height of an equilateral triangle in terms of its side s is s√3/2, the height of the triangle is 6√3/2 = 3√3 and so the area is (1/2)(6)(3√3) = 9√3. 

<span>If we draw a horizontal line a height of h from the base of the triangle, the region is split into two regions: the lower region consisting of a trapezoid of height h and the upper region consisting of a triangle of height 3√3 - h. </span>

<span>Since the upper triangle and the triangle itself are similar triangles, the base and height are proportional. If we let x denote the base of the length of the upper triangle, we have: </span>

<span>(S. of small triangle)/(S. of big triangle) = (Ht. of small triangle)/(Ht. of big triangle) </span>
<span>==> x/6 = (3√3 - h)/(3√3) </span>
<span>==> x = (6√3 - 2h)/√3 </span>

<span>Thus, the area of the upper triangle is: </span>

<span>A = (1/2)[(6√3 - 2h)/√3](3√3 - h) = [(6√3 - 2h)(3√3 - h)]/(2√3). </span>
<span>(Made a dumb mistake about the height here for some reason) </span>

<span>Since we require that the area of this triangle is to be half of the total area (9√3/2), we need to solve: </span>

<span>[(6√3 - 2h)(3√3 - h)]/(2√3) = 9√3/2 </span>
<span>==> (6√3 - 2h)(3√3 - h) = 27 </span>
<span>==> 54 - 6h√3 - 6h√3 + 2h^2 = 27 </span>
<span>==> 2h^2 - 12h√3 + 27 = 0. </span>

<span>Solving with the Quadratic Formula gives: </span>

<span>h = (6√3 + 3√6)/2 ≈ 8.87 units and h = (6√3 - 3√6)/2 ≈ 1.52 units. </span>

<span>Since h = (6√3 + 3√6)/2 would place the line outside of the triangle, we pick h = (6√3 - 3√6)/2. </span>

<span>Therefore, the line should be ==> (6√3 - 3√6)/2 units from the base. </span>

<span>I hope this helps! ^^ Brainliest Please?</span><span>
</span>
bulgar [2K]3 years ago
4 0

Answer:

The height of the triangles is  3* sqrt(3)

Step-by-step explanation:

To find the height of an equilateral triangles we can use the rule of 30-60-90 Triangles where:

Height : a* sqrt(3)

Shorter side: a

Hypotenuse: 2a

Where a is the side of the base or shorter side of the triangle. If you draw the height of an equilateral triangle to its base you bisect one of the angles in two 30 degrees angles. So we arrive to two  30 - 60 -90 triangles. The  height divides the side into segments of length 3. So following the 30-6090 rule, the measures of this triangles are:

Shorter side: 3

Hypotenuse: 6

Height : 3* sqrt(3)

This height is equivalent to the one of the equilateral triangle so the height of the equi triangle is  3* sqrt(3)

You might be interested in
Marcus is trying to make a rectangular picture frame from wood. He nails together two 10-inch pieces of wood and two 8-inch piec
wariber [46]

Answer:

Step-by-step explanation:

You have right triangles, so use the Pythagorean Theorem

x = length of diagonal

8² + 10² = x²

164 = x²

x = √164 = 2√41 ≅ 12.8 in

3 0
3 years ago
At a gas station, the price of a regular gas was $3.80 per gallon on monday. the price increased to $3.85 per gallon on tuesday.
notsponge [240]
Monday's gas, $3.80 rounded to the nearest tenth of a dollar would be $3.80 (its already there)
Tuesday' gas, $3.85 rounded to the nearest tenth of a dollar would be $3.90
Hope this helps!! and if you ever need anything else just ask! :)
4 0
3 years ago
Read 2 more answers
Solve the proportion. i need help.<br> x+3/6=8/3<br><br> x=?
stellarik [79]

Answer:

x = 2 1/6 (13/6)

Step-by-step explanation:

to solve the proportion you must first find the LCF or least common factor

that is 6

so turn 8/3 into 16/6 by multiplying it by 2/2

x + 3/6 = 16/6

then you subtract 3/6 from both sides

x = 13/6

x is 2 1/6

6 0
2 years ago
Read 2 more answers
Write as a unit rate. $300 per 6 hours. A 50 hours per dollar B $50 per hour C $0.20 per hour D 0.2 hours per dollar
jonny [76]
The correct answer is B) $50 per hour. Hope this helps!
4 0
3 years ago
Can someone help me with this one
astra-53 [7]

Answer:

79,200

158,400

5 0
3 years ago
Other questions:
  • Find x<br> Geometry homework. Please help!
    10·1 answer
  • A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5
    8·1 answer
  • Solution to the system of inequalities shown below:
    14·1 answer
  • Are 2,386 and 3,286 the same quantity?​
    9·2 answers
  • HELP PLEASE.........​
    5·1 answer
  • use the elimination method to solve the system of equations. choose the correct ordered pairs -x + y=-3 and 3x + 2y=9
    7·1 answer
  • The recursive rule for a sequence and one of the specific terms is given. Find the position of the given
    7·1 answer
  • How many people can fit in one car?
    13·1 answer
  • Lisa played soccer for 234 hours on Saturday and for 135 hours on Sunday. How many hours did she play soccer during the weekend?
    6·2 answers
  • Find the average rate of change of the exponential equation from x = 3 to x = 6
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!