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Which is a right triangle formed using a diagonal through the interior of the cube? A cube. The top face has points G, B, C, F a

Black_prince [1.1K]

Answer: The correct option is triangle GDC

Step-by-step explanation: Please refer to the picture attached for further details.

The dimensions give for the cube are such that the top surface has vertices GBCF while the bottom surface has vertices HADE.

A right angle can be formed in quite a number of ways since the cube has right angles on all six surfaces. However the question states that the diagonal that forms the right angle runs "through the interior."

Therefore option 1 is not correct since the diagonal formed in triangle BDH passes through two surfaces. Triangle DCB is also formed with its diagonal passing only along one of the surfaces. Triangle GHE is also formed with its diagonal running through one of the surfaces.

However, triangle GDC is formed with its diagonal passing through the interior as shown by the "zigzag" line from point G to point D. And then you have another line running from vertex D to vertex C.

6 0

3 years ago

Read 2 more answers

Please help asap 25 pts

aivan3 [116]

I think that the answer to the question is b

6 0

3 years ago

In a triangle, find the value of the remote exterior angle given the remote interior angles are 27 and 53 degrees

GenaCL600 [577]

Answer:

80°

Step-by-step explanation:

exterior angle = sum of two remote interior angles

27 + 53 = 80

5 0

3 years ago

529 = 50x+625 solve for x

cupoosta [38]

529 = 50x + 625

-96 = 50x

x = -1.92

8 0

3 years ago

Consider the following problem: A farmer with 950 ft of fencing wants to enclose a rectangular area and then divide it into four

Alina [70]

Answer:

Step-by-step explanation:

(a)

Suppose we came up with an ideology whereby we pick a value for the length including the length dividing the inside into 4 parts(5 parallel sides), then we can get the value for breath by using the following process.

Let assume the length of the rectangle is 50;

Then, the breath can be calculated as follows:

= 50 × 5 = 250 ( since the breath is divided into 5 parallel sides)

The fencing is said to be 950 ft

So, 950 - 250 = 700

Then divided by 2, we get:

= 700/2

= 350

So for the first diagram; the length = 50 and the breath = 350

The area = 50 × 350 = 17500 ft²

Now, let's go up a little bit.

If the length increase to 100;

Then 100 × 5 = 500

⇒ 950 - 500 = 450

⇒ 450/2 = 225

The area = 225 × 100 = 22500 ft²

Suppose the length increases to 150

Then 150 × 5 = 750

⇒ 950 - 750 = 200

⇒ 200/2 = 100

The area = 150 × 100 = 15000 ft²

The diagrams for each of the outline above can be seen in the image attached below.

(b) The diagram illustrating the general solution can be seen in the second image provided below.

(c) The expression for the total area A in terms of both x and y is:

Area A = x×y

(d) Recall that:

The fencing is said to be 950 ft.

And the length is divided inside into 5 parallel sides;

Then:

5x + 2y = 950 (from the illustration in the second image below)

2y = 950 - 5x

$y = \dfrac{950}{2} - \dfrac{5}{2}x$

$y = 475- \dfrac{5}{2}x$

(e)

From (c); replace the value of y in (d) into (c)

Then:

Area A = x×y

$f(x)= x\times ( 475 -\dfrac{5}{2}x)$

Open brackets

$f(x)= ( 475 x-\dfrac{5}{2}x^2)$

(f)

By differentiating what we have in (e)

$f(x)= ( 475 x-\dfrac{5}{2}x^2)$

$f'(x)= ( 475 (1)-\dfrac{5}{2}(2x))$

$f'(x)= 475 -5x$

$\implies 475 = 5x$

x = 475/5

x = 95

From (d):

$y = 475- \dfrac{5}{2}x$

$y = 475- \dfrac{5}{2}(95)$

$y =237.5$

∴

Area A = x × y

Area A = 95 × 237.5

Area A = 22562.5 ft²

5 0

3 years ago