Question

If the perimeter of a rectangle is expressed by 2x^2+5x+9 and the width is 2x^2+1, find an expression for the length.

Answer 1

Answer:

-x^2+5/2x+7/2 = L

Step-by-step explanation:

We know the perimeter of a rectangle is given by

P = 2(L + W)

Substitute what we know

2x^2+5x+9 = 2( L+  2x^2+1)

Distribute

2x^2+5x+9 = 2 L+  4x^2+2

Subtract 4x^2 from each side

2x^2-4x^2+5x+9 = 2 L+  4x^2-4x^2+2

-2x^2+5x+9 = 2 L+2

Subtract 2 from each side 2 from each side

-2x^2+5x+9-2 = 2 L+2-2

-2x^2+5x+7 = 2 L

Divide each side by 2

-2/2x^2+5/2x+7/2 = 2 L/2

-x^2+5/2x+7/2 = L