The length of the bd in the given triangle is 12 cm. This is obtained by applying the Pythagoras theorem.
What is the Pythagoras theorem state?
The Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. I.e., [tex]a^2+b^2=c^2[/tex].
Given data from the diagram:
The triangle is perpendicularly divided into two halves looking like right-angled triangles.
The side lengths for the given triangle are bc=13 cm and ac=10 cm
Finding the length of the arm bd:
The line segment bd divides the triangle into two right-angled triangles symmetrically.
So, the base ac of the given triangle is divided at the mid-point d.
Thus,
ac = ad + dc
here, d is the mid point, ad = dc
So, ad=dc=5 cm
Now, the triangle forms a right-angled triangle with sides bd, dc, and bc. Where bc is the hypotenuse.
To find the length of bd, applying the Pythagoras theorem
[tex](bc)^2=(bd)^2+(dc)^2[/tex]
⇒ [tex](13)^2 = (bd)^2 + (5)^2[/tex]
⇒ [tex]169 = (bd)^2 +25[/tex]
⇒ [tex](bd)^2 = 169 - 25[/tex]
⇒ [tex](bd)^2 = 144[/tex]
∴ bd = 12 cm
Therefore, the length of the bd is 12 cm.
Learn more about Pythagoras's theorem here:
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