Question

Need help figuring out this problem. Please help, it is quick. Medal to best answer.

In triangle ABC if BC is one inch longer than AB, overline AC is 10 inches shorter than the sum of BC and AB and the perimeter of triangle ABC is 72 inches, find the length of BC

21 in
20 in
31 in
32 in

Answer 1

start by writing all the sides in terms of AB
You have

AB

BC = AB + 1

AC = AB + BC - 10 substitute BC and AC = AB + AB + 1 - 10

AC = 2AB - 9

you know the perimeter so

72 = AB + BC + AC

or

72 = AB + AB + 1 + 2AB - 9

which simplifies to

72 = 4AB - 8

now solve for AB

then you can find the other sides.

hope it makes sense

Answer 2

Thanks so much! That does make sense! I had come up with the first part but then I didn't know how to continue. So, I found that AB = 20. Then I plug that into BC = AB + 1. So 20 +1 = 21. So BC = 21 which is the answer. Is that correct?

Answer 3

thats correct.

Answer 4

THANK YOU SO MUCH!!