Shown is a cube of side length 8. Points B and C are midpoints. The length of the altitude from A to BC (bar over BC) of triangle ABC is ab√ where b√ is reduced to simplest form. What is a+b?

If D is the vertex on the bottom face of the cube below ∆ABC, then ∆BCD is an isosceles right triangle with legs of length 4, so BC has length 4√2.

The right triangles ∆ABD and ∆ACD both have legs of length 4 (on the bottom face) and 8 (the length of AD) so the hypotenuses AB and AC each have length √(4² + 8²) = 4√5.

Then in ∆ABC, the altitude has length x such that

(4√5)² = x² + (1/2 × 4√2)²

80 = x² + 8

x² = 72

x = √72 = 6√2

Presumably, you meant to say that this altitude has length a√b. Then a = 6 and b = 2, so a + b = 8.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!