The perimeter of a triangle with 2 equal sides is 46 cm. If its base were lengthened by 3 cm and each leg were shortened by 5 cm, all 3 sides would be equal. Find the length of the base of the original triangle.

Question

mathstudent55 · Answer

Perimeter = sum of lengths of three sides
A triangle with two equal sides is called an isosceles triangle. The two equal sides are the legs, and the third side is the base.
Let B = base and L = leg

From the perimeter you know:
        B + L + L = 46
or     B + 2L = 46

From the second statement, you know:
        B + 3 = L - 5
or     B + 8 = L

You have a system of two equations with two unkowns:
        B + 2L = 46
        B + 8 = L

Substitute what L is equal to in the second equation into L of the first equation.
        B + 2(B + 8) = 46
        B + 2B + 16 = 46
        3B = 30
        B = 10
The base is 10 cm long

Check: B + 8 + L; !0 + 8 = L; L = 18; the original base is 10 cm and the original legs are 18 cm. If you lengthen the base by 5 cm, the base will be 15 cm. If you shorten the legs by 3 cm, they will be 15 cm like the new base.