How do you do this?

Question

Im doing geometry and they asked me an algebra question but I don't remember how to do it. Can you help me?

The problem is AC=21, AB=x+13, and BC=x+12. Find BC.

any sort of help is highly appreciated.

Thanks

Answer 1

By the Segment Addition Postulate we have:

A--------------B------------C

AB = x+13

BC = x+12

AC = 21

AB + BC = AC

x+13 + x+12 = 21

2x + 25 = 21

Can you complete it?

Answer 2

The question is asking you to use the 'Segment Addition Postulate'.

If you draw out line segment labeled AC and mark 'B' as a point in the middle you will be able to see that AB + BC = AC

With that being said, take the equations that represent each line segment, and plug them into the equation I wrote above and solve for 'x'.

Once you solve for 'x' you just need to plug that back into the equation for 'BC'.

Answer 3

If it is a right triangle, then you can use the Pythagorean Theorem to write an equation relating the 3 sides.

If it is NOT a right triangle, I'm not sure how to solve it......

Example:

Suppose it IS a right triangle and AC is the hypoteneuse. You would then write this equation:

21² = (x + 13)² + (x +12)²

Expand this, simplify, and put in the standard quadratic form, and solve using one of the standard methods