Latest Elitmus Aptitude Question SOLUTION: P is a point inside a triangle ABC and its distance from three vertices A,B,C are 6,8,11 respectively.What could be perimeter of the triangle?

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Geometry

Elitmus Question Papers:

(#M40034967) ELITMUS Numerical Ability question Geometry Keep an EYE

P is a point inside a triangle ABC and its distance from three vertices A,B,C are 6,8,11 respectively.What could be perimeter of the triangle?

Asked In Elitmus (10 years ago)

Unsolved Read Solution (8)

Is this Puzzle helpful?   (5)   (2) Submit Your Solution Geometry

Read Solution (8) :

RAKESH  (10 years ago)

if x,y,z are the sides of triangle then
using,
a + b > c in 3 triangles
x < (6+8)
y < (8+11)
z < (11+6)
adding
=> (x+y+z) < 50

perimeter of the triangle will be just less than 50 .

Is this solution Helpfull? Yes (53) | No (3)  

Ashutosh  (10 years ago)

take a point P inside the triangle.u will get three triangles.draw perpendicular through P on their respective side..and apply Pythagoras
on AB after perpendicular devides it into x nd y
u will get
6^2=P^2+X^2
8^2=P^2+Y^2
by solving u will get X+y=14
lly u will get other sides.17 na 19
so perimeter=14+17+19=50

Is this solution Helpfull? Yes (3) | No (7)  

Aashish Bhatla  (10 years ago)

let the three sides be x, y, z

x < 6 + 8, i.e., x < 14 ... eq 1

y < 6 + 11, i.e., y < 17 ... eq 2

z < 8 + 11, i.e., z < 19 ... eq 3


Adding the equations eq1, eq2, eq3 :
x + y + z = Perimeter of triangle < 50

check options and mark the answer below 50

Is this solution Helpfull? Yes (2) | No (3)  

Raj Kumar Ray  (10 years ago)

but how did u get x+y=14 ?? from that two eqns.

Is this solution Helpfull? Yes (1) | No (2)  

Ashutosh  (10 years ago)

when u got triangles,APB
1.draw perpen from p to AB
2.apply Pythagoras theorem
3.solve equation interms of X^2-Y^2.....i.e X+Y nd X-Y
4.u will eaisly get X+y

Is this solution Helpfull? Yes (1) | No (5)  

ravi singh  (10 years ago)

here formula used are a^2 = b^2 + c^2 - 2*a*c here a is unknown side
so AB= (64+121-176)^(1/2)=3
BC= (64+36-96)^(1/2)=2
CA= (121+36-132)^(1/2)=5
hence perimeter is 3+2+5=10

Is this solution Helpfull? Yes (1) | No (9)  

raushan kumar  (10 years ago)

perimeter

Is this solution Helpfull? Yes (1) | No (3)  

vikrant gupta  (9 years ago)

join PA,PB,PC

Simple by rule of triangle in triangles PAB,PAC,PBC

PA+PB>AB

PB+PC>BC

PA+PC>AC

Now it’s given PA=6, PB=8, PC=11

So, 14>AB , 19>BC, 17>AC

Adding the three we get:

14+19+17>AB+BC+AC

=>50>AB+BC+CA

Is this solution Helpfull? Yes | No (2)  

Please Login to Read Solution.