Respuesta :
(2x^2+13x+15)/2x+3=x+5
Use long or synthetic division to solve this problem.
Answer : The length of the base of the parallelogram is, [tex]x+5[/tex]
Step-by-step explanation :
As we know that:
Area of parallelogram = Height × Base
Given:
Height of parallelogram = [tex]2x+3[/tex]
Area of parallelogram = [tex]2x^2+13x+15[/tex]
Now put all the given values in the above formula, we get:
Area of parallelogram = Height × Base
[tex]2x^2+13x+15[/tex] = [tex]2x+3[/tex] × Base
Base = [tex]\frac{2x^2+13x+15}{2x+3}[/tex]
Now factorize this expression [tex]2x^2+13x+15[/tex], we get:
Base = [tex]\frac{2x^2+(10x+3x)+15}{2x+3}[/tex]
Base = [tex]\frac{2x(x+5)+3(x+5)}{2x+3}[/tex]
Base = [tex]\frac{(2x+3)(x+5)}{2x+3}[/tex]
Base = [tex]x+5[/tex]
Therefore, the length of the base of the parallelogram is, [tex]x+5[/tex]
