Answer:
The base is 11 inches long
Step-by-step explanation:
we know that
An isosceles triangle has two equal sides and two equal interior angles
Let
y -----> is the length of the base of the isosceles triangle
x ----> is the length of each of the congruent sides
The perimeter of the triangle is equal to
[tex]P=y+x+x[/tex]
[tex]P=y+2x[/tex]
we have
[tex]P=55\ in[/tex]
so
[tex]55=y+2x[/tex] ----> equation A
[tex]y=\frac{x}{2}[/tex] ----> equation B
solve the system by substitution
substitute equation B in equation A
[tex]55=\frac{x}{2}+2x[/tex]
solve for x
[tex]55=\frac{5}{2}x[/tex]
[tex]x=55(2)/5\\x=22\ in[/tex]
Find the value of y
[tex]y=\frac{x}{2}[/tex] ----> [tex]y=\frac{22}{2}=11\ in[/tex]
therefore
The base is 11 inches long
