Question

Taryn is making a quilt using fabric in the shape of parallelograms that have side lengths of 12 cm and 4.5 cm as shown. She sews two right

triangles to either end of the parallelogram to make a rectangle. The length of OP is 2.5 cm.

What is the length of MN?

O A V2.5 cm

OB. 14 cm

OC 4.5 cm

OD 26.5 cm

OE 7 cm

Answer 1

`MN = \sqrt{14`

Explanation:

Given

`NO = 12`

`OP = 2.5`

`OQ = 4.5`

Required

Find MN

First, we calculate QP using Pythagoras theorem

`OQ^2 = OP^2 + QP^2`

`4.5^2 = 2.5^2 + QP^2`

`20.25 = 6.25 + QP^2`

Collect like terms

`QP^2 = 20.25 - 6.25`

`QP^2 = 14`

Take square roots

`QP = \sqrt{14`

To solve MN, we have:

`MN = OP`

So:

`MN = \sqrt{14`