Question

ABCD is a rhombus. Find AB. Enter your answer as a fraction in simplest form.

4x + 15
с
12yº
(2y - 2)°
7x + 2
AB =

Answer 1

`AB= (97)/(3)`

Explanation:

Properties of Rhombus

• All sides of the rhombus are equal.
• The opposite sides of a rhombus are parallel.
• Opposite angles of a rhombus are equal.
• In a rhombus, diagonals bisect each other at right angles.
• Diagonals bisect the angles of a rhombus.

We are given two sides of the rhombus BC and CD. According to the first property:

4x + 15 = 7x + 2

Subtracting 4x:

15 = 3x + 2

Subtracting 2:

13 = 3x

Dividing by 3:

`x=(13)/(3)`

It's required to find the side AB. Applying the first property again:

AB= BC = CD = 4x + 15

`AB =4*(13)/(3)+15`

`AB= (52)/(3)+15`

`AB= (97)/(3)`