Solve for x...?

Question

x (x * 4) = 400

How would I figure this one out? I am pretty bad @ Algebra! ^_^

I'm sorry...I think that equation was wrong...here is the entire problem :(

http://i53.photobucket.com/albums/g68/jec528/EX21P386.jpg

For a regular square pyramid, the slant height of each lateral face has a measure equal to that of the edges of the base. If the lateral area is 200 in.^2, find the volume of the pyramid.

Answer 1

I think you would do this by first multiplying out the left side. x(x*4) = x * 4x = 4x^2. The equation is then 4x^2 = 400. Divide both sides by 4 to get x^2 = 100. Then take the square root of both sides to get x=10. I'm not sure why the left hand side is written that way (it seems strange to me), but if that's correct, then this should be the answer. Do you see the basic process? I hope this helps.

Edit for new info provided: I had to look up some definitions and stuff, and used the site referenced below to help. If I understand it correctly, I think you were close with the equation. The sides of the pyramid have a slant height (point of triangle down to center of base) that's equal to a side of the base of the pyramid. If we call that x, then the lateral faces have bases = x and slant height = x. The area of these triangles are 200 in^2; I think that's per lateral face, not the total of all four. The area of a triangle is (1/2)*b*h, giving 200 = (1/2)*x*x; 200 = (x^2)/2; 400 = x^2; x = 20 in.

I'll try to help on the volume part, but it's been ages since I did this stuff, so I could have it wrong. You need the height of the pyramid to get the volume using V = (1/3)*b^2*h. In this case, b = x = 20 in, the length of one side of the square base. We need to find h. I think you get this by looking at a triangle inside the pyramid, as shown in the drawing you linked to. h is the center height, the line from the center of the base to the center of the edge of one side of the base is x/2 (the full side is x, and this is half that). The slant height is also x, and that's the third side of this triangle. Using the basic formula for triangles that a^2 + b^2 = c^2, where here a=x/2, b=h, and c=x; we have (x/2)^2 + h^2 = x^2 --> (x^2)/4 + h^2 = x^2 --> h^2 = x^2 - (x^2)/4, and h is the square root of the right side. Plugging in numbers (x=20), I get h = 17.32 in. Then the volume of the pyramid should be (1/3)*20^2*17.32 = about 2309 in^3.

Please check this to make sure that it looks right and makes sense to you. The basic procedure should be right, so if there is a mistake in my math somewhere, hopefully you can correct it. I hope this helps.

Answer 2

X * X * 4 = 400

divide both sides by 4

X^2 = 100

X = +10, -10

Answer 3

x(4x)=400

4x^2=400
divide by 4 on both sides

x^2 = 400/4=100

x= +10, -10

Answer 4

x (x*4) = 400

First, you simplify

x*4x = 400

then multiply

4x^2 = 400

divide both sides by 4

x^2 = 100

Take the square root of both sides.

x = 10

Answer 5

= 4x^2 = 400
x^2 = 100
x = 10 or -10

Answer 6

multiply to get 4x^2=400
next divide by 4 to get x^2=100
finally take the square root to get x=+10, -10

Answer 7

all i did was multiplied 4*10 which is 40 and 40*10=400 so x=10

Answer 8

x(4x) = 400
x*x= 400/4 =100
thus x = square root of (100)
= 10.

Answer 9

4x squared =400
x squared =100
x=10