First, you have to find out the values of the length and width.
Let l = length and w = width.
Set up your equation for area: l * w = 80
Set up your equation for perimeter: 2l + 2w = 36
We can use substitution for this problem, so find out the value of l or w. In this case, I will use the first equation to find out the value of l.
(Divide w on both sides) l = 80 / w
Since I know that l = 80 / w, I can substitute it into the second equation.
2l + 2w = 36, and l = 80 / w
= 2 (80/w) + 2w = 36
Simplify the equation.
= 160/w + 2w = 36
Get rid of the w in the denominator by multiplying the entire equation by w.
= ( 160/w + 2w = 36 ) * w
= 160 + [tex]2w^{2}[/tex] = 36w
= 2 ( w - 8 ) ( w - 10 )
The solutions for width (w) is 8 or 10. Then, you can use both 8 and 10 as your length and width, either or is fine. Multiply by 4 for each of those values and you get 8 x 4 = 32 and 10 x 4 = 40. The new perimeter would be 2(32) + 2(40) =
a. 144 cm
Hope this helped you! Let me know if there are any confusions :)
