Please see the question below.

A parallelogram is formed by vectors `barOA`=(2,3) and `barOB`=(1,1)

a)What are the lengths of the diagonals.

b) Find the perimeter of the parallelogram.

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To find the diagional, I have done this

(2,3)+(1,1)

=(3,4)

`sqrt(3^2+4^2)`

=5cm

Therefore the length of diagonal is 5 cm.

How to find the perimeter?

### 2 Answers | Add Yours

The diagional is:

(2,3)-(1,1)=(1,2)=sqrt(5) about2.236

OA=(2,3)=sqrt(13) about 3.606

OB=(1,1)=sqrt(2) about 1.414

The perimeter is 2*(OA+OB) about 10.04

You need to find the resultant vector bar (AB) such that:

`bar (AB) = <2 + 1, 3 + 1> => bar (AB) = <3,4>`

You need to evaluate the length of diagonal `AB` , hence, you need to evaluate the magnitude of the vector `bar (AB)` , such that:

`(AB) = sqrt(3^2 + 4^2) => (AB) = 5`

Hence, evaluating the length of diagonal AB, using the information provided by the problem, yields `(AB) = 5.`

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