Question

The perimeter of a rectangle is 28x³ + 16x² + 8x + 4. One of its side is 8x²+ 4x. Find the other side.

Answer should be 14x³+2

Answer 1

Let another side of the rectangle be B.
We have ,
perimeter = 28x^3 + 16x^2 + 8x + 4
side1 = 8x^2 + 4x

now we know the perimeter of a rectangle is given by 2(side1+side2)
thus substituting above values we get
2(8x^2+4x+B)=28x^3 + 16x^2 + 8x + 4
16x^2 + 8x + 2B = 28x^3 + 16x^2 + 8x + 4
2B= 28x^3 + 16x^2 + 8x + 4 - 16x^2 - 8x
2B = 28x^3 + 4
B = 14x^3 + 2

Thus another side is 14x^3 + 2