Answer:
The original triangle has sides of 18 cm, 18 cm and 10 cm
Step-by-step explanation:
Let x cm be the length of the leg of the original triangle and y cm be the length of the base of the original triangle.
1. Since the perimeter of the original triangle is 46 cm, then
x+x+y=46.
2. If it's base were lengthened by 3 cm, then it becomes y+3 cm. If each leg were shortened by 5 cm, then each leg becomes x-5 cm. All three sides became equal, then
y+3=x-5.
3. Solve the system of two equations:
[tex]\left\{\begin{array}{l}2x+y=46\\x-5=y+3\end{array}\right.\Rightarrow \left\{\begin{array}{l}2(y+8)+y=46\\x=y+8\end{array}\right.,\ 2y+y=46-16,\ 3y=30,\ y=10\ cm.[/tex]
Then [tex]x=10+8=18\ cm.[/tex]
