Question

Given BE = 2x + 6 and ED = 5x - 12 in

parallelogram ABCD, find BD.

Answer 1

Given the statement: BE = 2x + 6 units and ED = 5x - 12 units.

By properties of parallelogram:

The parallelogram bisects each other at E.

You can see the diagram of parallelogram as shown below.

Therefore;

`BE =ED` .....[1]

Substitute the given values we have;

`2x+6 = 5x-12`

Add 12 both sides we get;

`2x+18= 5x`

Subtract 2x from both sides we have;

`18= 3x`

Divide 3 both sides we get;

x = 6.

BE = 2x+6 = 2(6)+6 = 12 +6 = 18 units

We have to find the value of BD:

BD = BE+ED

from [1] we have;

`BD = 2BE`

`BD = 2 \cdot 18 = 36 units`

Therefore, the value of BD is, 36 units.