Derrick cut a square cake vertically to make two rectangle slices. Each rectangle had a perimeter of 51 inches.

17 inches

Step-by-step explanation:

Given

--- Perimeter of rectangle

Required

The length of the original square

The perimeter is calculated as

Divide by 2

The rectangle and the square have the same length.

So:

becomes

Divide both sides by 3

Recall that:

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step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2