contestada

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?

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 si class=

Respuesta :

LammettHash

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.

abidemiokin

The measure of a + b given that [tex]a\sqrt{b} = 6\sqrt{2}[/tex] is 8

From the given diagram, we have that the side length of the cube is 8units.

Let the midpoint of BC is E. The required length will be AE

Get the hypotenuse AC using Pythagoras theorem;

AO = 8 units

OC = 3 units

Get the measure of AC

[tex]AC^2 = AO^2+OC^2\\AC^2=8^2+4^2\\AC^2=64+16\\AC^2=80\\AC^2=80\\AC=4\sqrt{5}[/tex]

Next is to get the length of BC using Pythagoras theorem:

[tex]BC^2=4^2+4^2\\BC^2=16+16\\BC^2=32\\BC = \sqrt{32}\\BC=4\sqrt{2}[/tex]

Get the measure of EC

[tex]EC=\frac{4\sqrt{2} }{2} \\EC=2\sqrt{2}[/tex]

Get the required length of AE using Pythagoras theorem;

[tex]AC^2=AE^2+EC^2\\(4\sqrt{5})^2= AE^2+(2\sqrt{2} )^2\\AE^2=80-8\\AE^2=72\\AE=\sqrt{72}\\AE =\sqrt{36\times 2}\\AE=6\sqrt{2}[/tex]

Compare with the radical function [tex]a\sqrt{b}[/tex], where a = 6 and b = 2, hence [tex]a+b= 6+2 =8[/tex]

Learn more here: https://brainly.com/question/11748505

Otras preguntas