What is the surface area of a right rectangular prism whose dimensions are 3 by 6 by 8?

All three sides of a triangle are initially 4 m in length. One of the triangle's sides is oriented horizontally. The triangle is

Arlecino [84]

Answer:

the new height of the triangle = 2.449

Step-by-step explanation:

Given that:

the sides of the triangle are 4m in length i.e they are equal. It shows that the triangle is known to be an equilateral triangle.

Let say the triangle is a triangle IJK

Let the length of the side to be i = 4

Definitely

IJ = JK = IK = i = 4

If a midline is drawn and cuts the equilateral triangle in two equal halves of a right-angle triangle. Then, suppose the midline is L

Then ;

$JL = \dfrac{1}{2} JK$

$JL = \dfrac{1}{2} i$

Let consider triangle IJL

(IL)² = (IJ)² - (JL)²

$(IL)^2 = i^2 - \dfrac{i^2}{4}$

$(IL)^2 = \dfrac{3i^2}{4}$

$(IL) =\sqrt{ \dfrac{3i^2}{4}}$

$IL =\sqrt{3} \dfrac{i}{2}$

Area of triangle IJK can be expressed as:

$Area = \dfrac{1}{2}\times Base \times Height$

$Area = \dfrac{1}{2}\times i \times \sqrt{3}\dfrac{i}{2}$

$Area = \sqrt{3}\dfrac{i^2}{4}$

where, i = 4

Then:

$Area = \sqrt{3}\dfrac{4^2}{4}$

$Area = \sqrt{3} \dfrac{16}{4}$

$Area =4 \sqrt{3}$

when the area is exactly half of the original triangle's area, the new height is :

$A = \dfrac{1}{2} \times Area$

$\sqrt{3} \dfrac{i^2}{4} = \dfrac{1}{2} \times 4\sqrt{3}$

$\dfrac{i^2}{4} = \dfrac{1}{2} \times 4$

$\dfrac{i^2}{4} =2$

$i^2 = 8$

$i= \sqrt{8}$

$i= \sqrt{4 \times 2}$

$i= 2 \sqrt{2}$

Finally, the new height of the new triangle is:

$IL =\sqrt{3} \dfrac{i}{2}$

$IL =\sqrt{3} \dfrac{2 \sqrt{2}}{2}$

$IL =\sqrt{3 \times 2}$

$IL =\sqrt{6}$

IL = 2.449 m

6 0

4 years ago

How many times can 18 go into 357

Tomtit [17]

18 goes into 357 19.84 times.

8 0

3 years ago

Read 2 more answers

(THIS IS 6TH GRADE MATH) PLEASE HELP<br>

garri49 [273]

Answer:

f(x)=(x sqrt(x))/(x-6)^2 is continous at x=36

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Laura buys an unfair coin online. The coin is supposed to land heads up 75% of the time. If this is true, what is the

Archy [21]

Answer:

C . (0.75) 15 x (0.25) 5

Step-by-step explanation:

Took the assignment in edge, it’s right

Its based off of the rule P(A and B) = P(A) x P(B) from multiplication rule for independent events.

4 0

3 years ago

How to find subtotal and sales tax? Give an example.

gizmo_the_mogwai [7]

Answer:

See explanation below.

Step-by-step explanation:

First, obtain the percentage of sales tax for a sale. Say it is 5%.

Then, obtain the sale prices, for two items say they are: $25.00 and $15.00.

Add the amounts together to obtain the subtotal:

$25.00 + $15.00 = $40.00, is the subtotal.

Multiply the amount by the percentage:

$40.00 * 5% =

40 * .05 = $2.00, is the sales tax

Add the tax to the subtotal to obtain the total amount to pay:

$40.00 + $2.00 = $42.00, is the total amount to pay.

Hope this helps!! Have an Awesome Day!! :-)

3 0

4 years ago