Construct a LMNO such that \[l({\rm{LM}}) = l({\rm{LO}}) = 6{\rm{ cm}},l({\rm{ON}}) = l({\rm{NM}}) = 4.5{\rm{ cm}},l({\rm{OM}}) = 7.5{\rm{ cm}}\]

Hint:
Here, we will construct a shape with the help of straight lines. We will first draw a straight line of given length LM. Then from the one end we will draw two arcs using the bisector to obtain a point. Similarly, we will draw the other two arcs using the bisector to obtain other points. Then by joining all the points we will be able to draw the shape LMNO.

Complete step by step solution:
It is given that the length of the sides of the rectangle LMNO is
\[l({\rm{LM}}) = l({\rm{LO}}) = 6{\rm{ cm}}\], \[l({\rm{ON}}) = l({\rm{NM}}) = 4.5{\rm{ cm}}\], \[l({\rm{OM}}) = 7.5{\rm{ cm}}\]
Firstly, we will draw a line of 6 cm length and name it as side LM.

Now from the end points of the given line, we have to draw two arcs using the bisector to obtain the point O.
We will draw an arc of length 6cm taking L as the center and draw an arc of length 7.5cm taking M as the center and cuts the other arc. The new point of intersection obtained is point O.
Now we will draw the line LO.

Now, we have to draw two arcs using the bisector to obtain the point N.
We will draw an arc of length 4.5cm taking O as the center and draw an arc of length 4.5cm taking M as the center and cuts the other arc. The new point of intersection obtained is point N.
Again we will draw the line ON and NM.

From the obtained we can see that it is a quadrilateral. Hence, the required quadrilateral LMNO is drawn.

Note:
Geometry is the branch of mathematics that deals with points, lines and shapes. In geometry, bisection is the division of something into two equal parts. Bisection is generally done with a line which is called a bisector. There are two main types of bisectors i.e. line segment bisector and angle bisector.
A line segment bisector is a line or line segment that divides the line into two equal parts or which passes through the midpoint of the line segment.
Angle bisector is the line or line segment that divides an angle into two equal parts. An angle has only one bisector. Also there are two types of angle bisectors i.e. interior and exterior angle bisector.