Answer:
4 x 4 x 8
Explanation:
So we have a birdhouse that is a recangular prism. This means the volume is simply depth * height * width. We are given that the depth is 4 inches, the width is w inches, and the height is 4 + w.
Set up a volume equation to represent the situtation
(4)(w)(4 + w) = 128
(w)(w + 4) = 32
w² + 4w = 32
Use "completing the square" to solve for w. If you don't know how...
ax² + bx + c represents a square function. Take the coefficient b, divide it by 2, and then square it. Add this number to both sides of the equation so that we create a factorable square polynomial while keeping the equation equal to the original.
w² + 4w + 4 = 32 + 4
Factor and simplify.
(w + 2)² = 36
w + 2 = ±6
w = ±6 - 2
w = -8, 4
The value -8 doesn't make sense as a dimension so the width is just 4.
Substitute this into our w + 4 that represents the height so the it is 8.
Now we can say the dimensions of the birdhouse are 4x4x8.