Question

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

Answer 1

Answer:

$BD = 30$

Step-by-step explanation:

Given

$AB = 17$

$AC = 16$

See attachment

Required

Find BD

If AC = 16, then:

$AO = 16/2$ i.e. half the diagonal AC

$AO = 8$

The diagonals of a rhombus are perpendicular.

This implies that we can apply Pythagoras theorem.

Using Pythagoras theorem on triangle AOB, we have:

$AB^2 = AO^2 + OB^2$

$17^2 = 8^2 + OB^2$

$289 = 64 + OB^2$

Collect like terms

$OB^2 = 289 - 64$

$OB^2 = 225$

Take positive square roots of both sides

$OB = 15$

To solve for BD, we use:

$OB = \frac{BD}{2}$ --- i.e. half the diagonal BD

$BD = 2 * OB$

$BD = 2 * 15$

$BD = 30$