Try this beautiful Problem on Geometry based on Right-angled triangle from AMC 10 A, 2018. You may use sequential hints to solve the problem.
Right triangle has leg lengths
and
. Including
and
, how many line segments with integer length can be drawn from vertex
to a point on hypotenuse
,
Geometry
Triangle
Pythagoras
Pre College Mathematics
AMC-10A, 2018 Problem-16
Given that is a Right-angle triangle and
and
. we have to find out how many line segments with integer length can be drawn from vertex
to a point on hypotenuse
?
Let be the foot of the altitude from
to
. therefore
is the shortest legth .
which is between
and
.
Now can you finish the problem?
let us assume a line segment with
on
which is starts from
to
. So if we move this line segment the length will be decreases and the values will be look like as
. similarly if we moving this line segment
from
to
hits all the integer values from
.
Now Can you finish the Problem?
Therefore numbers of total line segments will be
Try this beautiful Problem on Geometry based on Right-angled triangle from AMC 10 A, 2018. You may use sequential hints to solve the problem.
Right triangle has leg lengths
and
. Including
and
, how many line segments with integer length can be drawn from vertex
to a point on hypotenuse
,
Geometry
Triangle
Pythagoras
Pre College Mathematics
AMC-10A, 2018 Problem-16
Given that is a Right-angle triangle and
and
. we have to find out how many line segments with integer length can be drawn from vertex
to a point on hypotenuse
?
Let be the foot of the altitude from
to
. therefore
is the shortest legth .
which is between
and
.
Now can you finish the problem?
let us assume a line segment with
on
which is starts from
to
. So if we move this line segment the length will be decreases and the values will be look like as
. similarly if we moving this line segment
from
to
hits all the integer values from
.
Now Can you finish the Problem?
Therefore numbers of total line segments will be