A54-foot piece of siding is cut into three pieces so that the second piece is three times as long as the first piece and the third piece is five times as long as the first piece. if x represents the length of the first piece, find the lengths of all three pieces

The lenght of the first piece is 6 feet.

The lenght of the second piece is 18 feet.

The lenght of the third piece is 30 feet.

Step-by-step explanation:

Let be:

the lenght of the first piece (in feet).

the lenght of the second piece (in feet).

the lenght of the third piece (in feet).

You know that the total lenght of the  piece of siding is 54 feet. This means that:

Having this expression, you can solve for "x":

Therefore, the lenght of the first piece is 6 feet.

Then:

(The lenght of the second piece is 18 feet)

(The lenght of the third piece is 30 feet)

x = 17

step-by-step explanation:

in the given figure, two triangles are inscribed in a circle where ∠bae ≅ ∠dae which makes the side be and de equal so we can write it as:

3x - 24 = x + 10

solving this equation for x to get:

3x - x = 10 + 24

2x = 34

x = 34/2

x = 17

therefore, the value of x = 17.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)