Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes wi
# Engineering

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50 sq. units, then the number of elements in the set S is:-

Answers (1)
H Harsh Kankaria

Let the coordinates of the triangles be (0,0),(a,0),(0,b) where a,b \in I

Area of the triangle = \frac{1}{2}|ab| = 50

\Rightarrow |ab| = 100

100 as a product of two integers in first quadrant only

= n\{(1,100),(2,50),(4,25), (5,20),(10,10),(20,5),(25,4),(50,2),(100,1)\}

= 9

\therefore In all four quadrants = 9\times4 =36

Therefore, there are 36 elements in the set S

Similar Questions

Preparation Products

Knockout KCET 2021

An exhaustive E-learning program for the complete preparation of KCET exam..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout KCET JEE Main 2021

It is an exhaustive preparation module made exclusively for cracking JEE & KCET.

₹ 27999/- ₹ 16999/-
Buy Now
Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Rank Booster JEE Main 2020

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 9999/- ₹ 4999/-
Buy Now
Test Series JEE Main Sept 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 1999/-
Buy Now
Exams
Articles
Questions