Question

The perimeter of a triangle with two equal sides is 46 cm. If it's base were lengthened by 3 cm and each leg were shortened by 5 cm, all three sides would be equal. Find the length of the base of the original triangle

Answer 1

The original triangle has sides of 18 cm, 18 cm and 10 cm

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:

`\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.`

Then
`x=10+8=18\ cm.`