The base of an isosceles triangle is one half as long as each of the congruent sides. The perimeter is 55 in. How long is the base?

Answer:The base is 11 inches longStep-by-step explanation:we know thatAn isosceles triangle has two equal sides and two equal interior anglesLety -----> is the length of the base of the isosceles trianglex ----> is the length of each of the congruent sidesThe 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 Bsolve the system by substitutionsubstitute 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]thereforeThe base is 11 inches long