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nalin [4]
3 years ago
13

Find the area of an equilateral triangle with sides 6m.​

Mathematics
1 answer:
Likurg_2 [28]3 years ago
4 0

Answer:  12 m²

Step-by-step explanation:

Find height first:

It would be a 3-4-5 triangle, (or you could use Pythagorean theorem) so the height would equal 4.

Equation:

\frac{1}{2}bh = \frac{1}{2}(6)(4) = 12 m²

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(please answer if you know how to do this, it's due today !!) Solve for x, y and z. No links please
satela [25.4K]

Answer:

x = 4

y = 2√5

z = 3√5

Step-by-step explanation:

There are 3 right triangles here, so we can create 3 expressions using Pythagoras' Theorem:

a² + b² = c²

(where a and b are the legs, and c is the hypotenuse)

smallest triangle:  x² + y² = (x + 2)²

medium triangle: (x + 1)² + y² = z²

largest triangle: (x + 2)² + z² = (x + x + 1)²

rewrite the smallest triangle expression to make y² the subject:

x² + y² = (x + 2)²

⇒ x² + y² = x² + 4x + 4

⇒  y² = 4x + 4

rewrite the medium triangle expression to make z² the subject, substituting y² = 4x + 4:

(x + 1)² + y² = z²

⇒ (x + 1)² + 4x + 4 = z²

⇒ x² + 2x + 1 + 4x + 4 = z²

⇒ z² = x² + 6x + 5

rewrite the largest triangle, substituting z² = x² + 6x + 5 and solve for x:

(x + 2)² + z² = (x + x + 1)²

⇒ (x + 2)² + x² + 6x + 5 = (2x + 1)²

⇒ x² + 4x + 4 + x² + 6x + 5 = 4x² + 4x + 1

⇒  2x² - 6x - 8 = 0

⇒  x² - 3x - 4 = 0

⇒ (x + 1)(x - 4) = 0

⇒ x = -1, x = 4

as x > 0, x = 4 only

Substitute found value for x into y² = 4x + 4 and solve for y:

y² = (4 x 4) + 4

⇒ y² = 20

⇒ y = √20 = 2√5

Substitute found value for x into z² = x² + 6x + 5 and solve for z:

z² = 4² + (6 x 4) + 5

⇒ z² = 45

⇒ z = √45 = 3√5

8 0
3 years ago
Judy and her sister went together to get haircuts. Judy got 9 3/5 inches cut off and her sister got 4 1/10 inches cut off. Compa
disa [49]

Answer:

5 1/2

Step-by-step explanation:

9 3/5 - 4 1/10

First you need to get common denominator, as we see that we need to get the 5 from the 3/5 to ten, so we multiply 3/5 by 2 on both of the numerator and denominator and you will get 6/10. So the new fraction would be 9 6/10 - 4 1/10 = which would be subtractable. Therefore the answer would be 5 5/10 which equals

5 1/2

4 0
2 years ago
Read 2 more answers
Please help? It’s a basic time question and I don’t get it. Either I’m really dumb or it’s to complicated
Y_Kistochka [10]

Answer: D 1 hour 56 minutes

5 0
4 years ago
Read 2 more answers
Brainliest + Points! [Please explain]
garri49 [273]

Answer:

Step-by-step explanation:

10/12=.833

we know that there are 12 months in a year. so the %10 annually is evenly spread out whether it be daily monthly weekly. so just divide the %10 by 12.  

3 0
4 years ago
Two water pumps are filling a pool. One of the pumps is high power and can fill the pool 5 hours before the other can do. Howeve
9966 [12]

L = hours for the slower pump to fill the pool

L - 5 = hours for the high power pump, since it can do it in 5 hours less.

since the slower pump takes L hours, the faster pump takes then L - 5 hours.

we know both pumps together take 3 hours to do <u>half of the pool</u>, so that means that to fill up <u>the whole pool it takes them 6 hours</u>.

since the slower pump can do it alone in L hours, in 1 hour it has done 1/L of the whole thing.

likewise, since the faster pump can do it in L-5 hours, in 1 hour alone it has done 1/(L-5) of the whole job.


\bf \stackrel{\textit{slower pump's rate}}{\cfrac{1}{L}}~~~~+\stackrel{\textit{faster pump's rate}}{\cfrac{1}{L-5}}~~~~=~~~~\stackrel{\textit{total done in 1 hour}}{\cfrac{1}{6}} \\\\\\ \textit{let's multiply both sides by }\stackrel{LCD}{6(L)(L-5)}\textit{ to do away with the denominators} \\\\\\ 6(L)(L-5)\left( \cfrac{1}{L}+\cfrac{1}{L-5} \right)=6(L)(L-5)\left( \cfrac{1}{6} \right)


\bf 6(L-5)+6L=(L)(L-5)\implies 6L-30+6L \\\\\\ 12L-30=L^2-5L\implies 0=L^2-17L+30 \\\\\\ 0=(L-15)(L-2)\implies L= \begin{cases} \boxed{15}\\ 2 \end{cases}


now, we can't use L = 2, because, the whole job by both is done in 6 hours, there's no way the slower pump can do it in less than that, so L = 15.

now if L = 15, then L - 5 = 10.

5 0
4 years ago
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