Respuesta :

Someone2020

Answer:

12cm

Step-by-step explanation:

This is a problem which can be solved with the pythagoras therom.

[tex]a^{2} +b^{2} =c^{2}[/tex]

Plus we can split this triangle into two triangles.

The split triangle has dimensions of 13(bc) by 5 cm(dc).[tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]5^{2} +b^{2} =13^{2}[/tex]

Now we solve for b which is the lenght of bd

[tex]25 +b^{2} =169[/tex]

[tex]b^{2} =144[/tex]

[tex]b = \sqrt{144}[/tex]

[tex]b = 12[/tex]

Therefore the lenght of bd is 12cm

Hope this helps! :)

animallove2433
bd = 12

To start, you can see that this is a large triangle divided in half to create 2 right triangles. This means we can use the Pythagorean theorem (a^2) + (b^2) = (c^2) to find the segment bd.

To use the theorem we must know at least 2 values of the sides of the triangle. Since segment ac = 10 cm, we can divide this by 2 to get the base values of the smaller triangles, which would be 5 cm.

So a = 5 cm, c = 13 cm

Now, we have what we need and we can plug it in to the equation:

(5 cm)^2 + b^2 = (13 cm)^2

25 cm + b^2 = 169

b^2 = 144

b = 12 cm

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