One side of a triangle is 1 cm shorter than the base, x . The other side is 9 longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 20 cm?

Question

One side of a triangle is 1 cm shorter than the base, xx. The other side is 9 longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 20 cm?

I have to know this for math but I don't understand how to do it and I really need help ASAP.

Answer 1

x-1 + x+9 +x = 20

3x =20-8

x = 12/3 =4 cm

base must be at least 4 cm

but base also must be at least 10 cm

for 4 cm the other two sides are 3 and 13 which is impossible

as no side can be longer than the sum of the other 2 sides

with base = 10

the other sides are 9 and 19

9+10+19= 38>20

19=10+9=19

base has to be more than 10, b>10

if b=10 the "triangle" collapses into a line

Answer 2