Respuesta :
Answer:
The length is increased by 5 feet and width is increased by 7 feet.
Step-by-step explanation:
Given:
Length of section is twice the width.
During sale the section is expanded to an area = [tex](2w^2+19w+35)\ ft^2[/tex]
To find increase in length and width.
Solution:
Let the length of the section be = [tex]l\ ft[/tex]
width of the section = [tex]w\ ft[/tex]
Expression for area :
[tex]2w^2+19w+35[/tex]
Factoring:
[tex]2w^2+14w+5w+35[/tex]
[tex]2w(w+7)+5(w+7)[/tex]
[tex](2w+5)(w+7)[/tex]
So, area of the section after increase can be given as [tex](2w+5)(w+7)[/tex]
We know that length is twice the width, which means:
[tex]l=2w[/tex]
Substituting the value of [tex]2w[/tex] in the factored expression of area.
[tex](l+5)(w+7)[/tex]
Since area of triangle is product of length and width, so we have:
New length of section = [tex](l+5)\ ft[/tex]
New width of the section = [tex](w+7)\ ft[/tex]
Thus, length is increased by 5 feet and width is increased by 7 feet.
