Mathematics, 19.09.2019 05:00 jennemylesp19oy5

What is the slant height x of this square pyramid?
enter your answer in the box. express your answer in radical form.
x = m
explain how you solved it.

What is the slant height x of this square pyramid? enter your answer in the box. expres

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Answer from: Hooorax01

Since this is a square pyramid, the length of all the sides going up towards the top point of the pyramid (the apex) are all 4m. The triangular faces of the square pyramid are all equilateral triangles because we are given that one of the angles is 60°.

Since we are just looking for x, we can ignore all the other sides of the square pyramid except for the front face with x and 60°. That front face is an equilateral triangle. We see x splitting the equilateral triangle into two smaller triangles. These smaller triangles are all special 30-60-90 triangles (see picture), so you can use your rules for the side lengths of the triangles to figure out the length of x.

In a 30-60-90 triangle, the sides are in a 1:2:√3 ratio for the short leg to the long leg to the hypotenuse. That means the long leg is the short leg times 2 and the hypotenuse is the short leg times √3.

We know the hypotenuse is 4m and we are trying to find the long leg, x. We know that the ratio of the hypotenuse to the long leg is √3:2 and we can cross multiply and solve for x, then put x into simplest radical form:
$\frac{hypotenuse}{long \: leg} = \frac{ \sqrt{3}}{2} \\
 \frac{4}{x} = \frac{ \sqrt{3}}{2} \\
8 = x\sqrt{3}\\
x = \frac{8}{\sqrt{3}} \\ 
x = \frac{8}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\\
x= \frac{8\sqrt{3}}{3}$

Your final answer is $x= \frac{8\sqrt{3}}{3}$ .
What is the slant height x of this square pyramid? enter your answer in the box. express your answe

What is the slant height x of this square pyramid? enter your answer in the box. express your answe

Answer from: bbyggigi94041

The slant height of the given square pyramid is 2√3 m.

Step-by-step explanation: We are given to find the slant height of the square pyramid shown in the figure.

As modified in the attached figure, the pyramid consists of four congruent equilateral triangles with side length 4 m and a square base of side length 4 m.

ΔABC is one of the four triangles.

We are to find the value of x.

In ΔABC, AB = BC = CA = 4 m and AD ⊥ BC, so D will be the mid-point of BC because any altitude of an equilateral triangle divides the opposite side into two equal parts.

That is,

$BD=DC=\dfrac{1}{2}\times BC=\dfrac{1}{2}\times4=2.$

Now, from the right-angled triangle ABD, we have

$AB^2=BD^2+AD^2~~~~~\textup{[Using Pythagoras theorem]}\\\\\Rightarrow AD^2=AB^2-BD^2\\\\\Rightarrow x^2=4^2-2^2\\\\\Rightarrow x=\sqrt{16-4}\\\\\Rightarrow x=\sqrt{12}\\\\\Rightarrow x=2\sqrt3.$

Thus, the slant height of the given square pyramid is 2√3 m.

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

The operation is suck a c@ck? !

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