Question

Can someone correct my work?

Answer 1

Why are they similar triangles? If the line from A is perpendicular to BC then the hypotenuse (8), is smaller than `x+4`,(14)!

Explanation:

use Pythagoras

`BC^2=8^2+12^2`

`BC=sqrt(208)` = 14.4222051

`x+4+2x+1=sqrt208`

`3x=sqrt208 - 5`

`x=(sqrt208 - 5)/3`

x=3.140735034

Answer 2

`"correct"`

Explanation:

`"you have used the "color(blue)"angle bisector theorem"`
`"correctly and solved the corresponding equation"`

Answer 3

You're correct. I got `x=10` too.

Explanation:

I assume that's an angle bisector but it's not totally clear from the figure.

We can write the Bisector Theorem a couple of different ways; they all work out the same. Let's do it this way:

`{x+4}/8 = {2x+1}/12`

`12(x+4) = 8(2x+1)`

`12x + 48 = 16x + 8`

`40 = 4x`

`x = 10`

Now I can check yours. You did better than me, reducing the fraction first. I'm a little more terse with my algebra.

You're not buying yourself anything with "the value of x is equivalent to 10." What's "equivalent to ten" mean anyway? Write `x=10`, maybe put a box around it, and go on to the next problem.