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In rhombus ABCD shown below, AB=17 and AC=16 determine the length of BD without (hint , not with trigonometry)

Sagot :

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]

View image MrRoyal
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