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# Right-angled Triangle | AMC 10A, 2018 | Problem No 16

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-angled triangle - AMC-10A, 2018- Problem 16

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

## Suggested Book | Source | Answer

Pre College Mathematics

#### Source of the problem

AMC-10A, 2018 Problem-16

## Try with Hints

#### First Hint

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?

#### Second Hint

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?

#### Third Hint

Therefore numbers of total line segments will be

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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-angled triangle - AMC-10A, 2018- Problem 16

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

## Suggested Book | Source | Answer

Pre College Mathematics

#### Source of the problem

AMC-10A, 2018 Problem-16

## Try with Hints

#### First Hint

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?

#### Second Hint

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?

#### Third Hint

Therefore numbers of total line segments will be

## Subscribe to Cheenta at Youtube

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