Answer:
[tex]BD = 30[/tex]
Step-by-step explanation:
Given
[tex]AB = 17[/tex]
[tex]AC = 16[/tex]
See attachment
Required
Find BD
If AC = 16, then:
[tex]AO = 16/2[/tex] i.e. half the diagonal AC
[tex]AO = 8[/tex]
The diagonals of a rhombus are perpendicular.
This implies that we can apply Pythagoras theorem.
Using Pythagoras theorem on triangle AOB, we have:
[tex]AB^2 = AO^2 + OB^2[/tex]
[tex]17^2 = 8^2 + OB^2[/tex]
[tex]289 = 64 + OB^2[/tex]
Collect like terms
[tex]OB^2 = 289 - 64[/tex]
[tex]OB^2 = 225[/tex]
Take positive square roots of both sides
[tex]OB = 15[/tex]
To solve for BD, we use:
[tex]OB = \frac{BD}{2}[/tex] --- i.e. half the diagonal BD
[tex]BD = 2 * OB[/tex]
[tex]BD = 2 * 15[/tex]
[tex]BD = 30[/tex]
