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nasty-shy [4]
1 year ago
15

Find the area of an equilateral triangle with 12-inch altitudes

Mathematics
1 answer:
Nina [5.8K]1 year ago
4 0

\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{side's}{length}\\[-0.5em] \hrulefill\\ h=12 \end{cases}\implies 12=\cfrac{s\sqrt{3}}{2}\implies 24=s\sqrt{3}\implies \cfrac{24}{\sqrt{3}}=s \\\\[-0.35em] ~\dotfill

\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}\qquad \qquad A=\cfrac{~~ \left( \frac{24}{\sqrt{3}} \right)^2 \sqrt{3}~~}{2}\implies A=\cfrac{~~ \frac{24^2}{3} \sqrt{3}~~}{2} \\\\\\ A=\cfrac{192\sqrt{3}}{2}\implies A=96\sqrt{3}\implies A\approx 166.28

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3/4=j-1/2 solve the equation check your solution
DIA [1.3K]
3/4= j-1/2
first to add 1/2 to both sides to solve for j 
3/4 + 1/2= j
second you find a common denominator in order to add 3/4 and 1/2, the common denominator would be 4, you would have to change 3/4 at all because the denominator is already 4 but in order to make the denominator of 1/2, 4 you would have to multiply both the denominator and numerator by 2 so 
3/4 + 2/4 = 5/4
so 5/4 =j

to check your answer you plug 5/4 in for j 
3/4 = 5/4 -1/2
again you need to find a common denominator between 5/4 and 1/2 which again would be 4, and again you wouldn't change 5/4 but you would multiply both the numerator and the denominator of 1/2 so 
3/4= 5/4-2/4
5-2= 3 and you would keep the 4 so 
5/4 - 2/4 = 3/4

so j =  5/4
5 0
2 years ago
Nancy shot a 24 on 4 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes?
Elden [556K]

Answer:

  108

Step-by-step explanation:

"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:

  score/18 = 24/4

Multiplying by 18, we get ...

  score = 18(24/4) = 18(6) = 108

Nancy can expect a score of 108 on 18 holes.

4 0
2 years ago
You have 192 grams of a radioactive kind of iodine. How much will be left
m_a_m_a [10]

Answer:

192/2= 96 g after 7h

96/2=48 g after 14h

48/2= 24 g after 21h

<h2>24/2= 12 g after 28h </h2>
8 0
3 years ago
in one day Annie traveled 5 times the sum of the number of hours Brian traveled and two together they travel 20 hours find this
Stels [109]

Use the distributive property:

5*b+5*2+b=20

5b+10+b=20.

Combine like terms:

6b+10=20.

Subtract 10 from both sides:

6b+10-10=20-10

6b=10.

Divide both sides by 6:

6b/6=10/6

b=5/3=1 2/3.

Brian travels 1 2/3 hours. This means Annie travels

5(1 2/3+2)=5(3 2/3)=5(11/3)=55/3=18 1/3 hours.

Hope this helps!

3 0
2 years ago
Read 2 more answers
Virginia Beach is 10 miles wide and 30 miles long. If one inch of rain falls on Virginia Beach, how many cubic feet of rain fell
Arte-miy333 [17]

1 mile = 5280 feet.

Convert the dimensions to feet:

10 miles = 5280 x 10 = 52,800 feet

30 miles = 5280 x 30 = 158,400 feet

Multiply together to get the area:

52,800 x 158,400 = 8,363,520,000 square feet.

1 inch = 1/12 of a foot.

Multiply the area by 1/12 for the volume of rain:

8,363,520,000 x 1/12 = 696,960,000 cubic feet.

3 0
3 years ago
Read 2 more answers
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