Answer:
Base = 35 inch
Step-by-step explanation:
Given that the triangle is an isosceles triangle;
The length of the two sides is: 12b - 8
The length of the base is: 9b + 8
Perimeter = 91 inches
Required
Calculate the length of the base;
The perimeter of a triangle is gotten by adding the length of the three sides.
So, in this case; we have
[tex]Perimeter = 12b - 8 + 12b - 8 + 9b + 8[/tex]
Collect like terms
[tex]Perimeter = 12b + 12b + 9b - 8 - 8 + 8[/tex]
[tex]Perimeter = 33b - 8[/tex]
Substitute 91 for Perimeter
[tex]91 = 33b - 8[/tex]
Add 8 to both sides
[tex]91 + 8 = 33b - 8 + 8[/tex]
[tex]99 = 33b[/tex]
Divide both sides by 33
[tex]\frac{99}{33} = \frac{33b}{33}[/tex]
[tex]3 = b[/tex]
[tex]b = 3[/tex]
Recall that the base of the triangle is 9b + 8
Base = 9b + 8
Substitute 3 for b
Base = 9(3) + 8
Base = 27 + 8
Base = 35 inch
