We are given $AB=7cm$, $BP=4cm$, $AP=5.4cm$ and we are told to compare the segments. Comparing the segments means to arrange in order from bigger to smaller. So, see the numbers and arrange from bigger to smaller. Then taking the reference of numbers arrange the segments $AB,AP$ and $BP$. Try it, you will get the answer.
Complete step-by-step answer:
In geometry, a line segment is a part of a line that is bounded by two distinct endpoints, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.
Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (of that polygon or polyhedron) if they are adjacent vertices, or otherwise a diagonal. When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve).
In geometry, a line can be defined as a straight one- dimensional figure that has no thickness and extends endlessly in both directions.
It is often described as the shortest distance between any two points.
A line is one-dimensional. It has zero width. If you draw a line with a pencil, examination with a microscope would show that the pencil mark has a measurable width. The pencil line is just a way to illustrate the idea on paper. In geometry however, a line has no width.
A straight line is the shortest distance between any two points on a plane.
Line, Basic element of Euclidean geometry. Euclid defined a line as an interval between two points and claimed it could be extended indefinitely in either direction. Such an extension in both directions is now thought of as a line, while Euclid’s original definition is considered a line segment. A ray is part of a line extending infinitely from a point on the line in only one direction. In a coordinate system on a plane, a line can be represented by the linear equation $ax+by+c=0$. This is often written in the slope-intercept form as $y=mx+b$, in which $m$is the slope and $b$ is the value where the line crosses the$y$ -axis. Because geometrical objects whose edges are line segments are completely understood, mathematicians frequently try to reduce more complex structures into simpler ones made up of connected line segments.
In the question we are given the length of segments $AB=7cm$, $BP=4cm$, $AP=5.4cm$.
Comparing the segments means to arrange in order from bigger to smaller.
Here, we can see that,
$AB=7cm$, $BP=4cm$, $AP=5.4cm$,
So, arranging the numbers from bigger to smaller we get,
So we get,
$AB>AP>BP$ i.e. $BPSo we get the correct answer as option (B).
Note: Read the question in a careful manner. Also, do not miss any term while arranging. Do not confuse yourself with the greater and smaller signs. Your concept regarding segments should be cleared. You must know that, comparing the segments means to arrange in order from bigger to smaller.