Latest Elitmus Aptitude Question SOLUTION: If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ABC is

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(#M40021005) ELITMUS Numerical Ability question Keep an EYE

If length of the sides AB, BC and CA of a triangle are 8cm, 15 cm and 17 cm respectively, then length of the angle bisector of ABC is

Asked In Elitmus saurabh saraff (10 years ago)

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mohan  (10 years ago)

10.5 bcz from the given data it is right angled triangle (satisfies pithogorous theoram ) now if angle bisector of 'a' will splits line BC 15 in to two equal parts... now apply pythogorus theoram here again between newly formed triangle AB,BC',C'A (c' is angle bisector of A) then we will get 10.5

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saurav kumar  (9 years ago)

(120 root2)/23

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NITHISH  (8 years ago)

Given triangle is Right angled at B
Length of Angle bisector of angle ∟ABC is
(2*c*a)*cos(B/2)/(c+a)=(2*8*15)*cos(45)/(8+15)=(2*120/23)*(1/√2)=(120*√2)/23

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tri  (10 years ago)

length of angle bisector in rt triangle is (2ca cos( b/2)) / c+a .. it will not bisect the hypotenuse. ans (120 root 2 )/ 3

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SHANUR RAHMAN  (8 years ago)

as the given sides are of pythagoras triplets (8,15,17)..
sotriangle ABC is a right angled triangle, right angled at B..

as angle bisector of ABC will bisect the angle only... so draw a line from B to AC (say D)and it makes..

NOW the angle anglDBC=ANGLDBA=45

now a property of angle bisector,
AB/BC=AD/CD
8/15=AD/CD
AS AC IS 17
AD=(8/23)*17= 5.9
NOW WE KNOW TWO SIDES OF TRIANGLE ABD AND ONE ANGLE IS 45
WE CAN USE COSINE RULE AND WE WILL GET BD

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Yogendra Kumar  (8 years ago)

8,15 and 17 are sides of a right angle triangle and ABC is a right angle.the angle bisector of abc will be perpendicular(say X) on side AC.
now,
1/2*8*15 = 1/2*X*17(area of triangle)
after solving this we get X=7.06

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shrishti singh  (8 years ago)

a=15,b=17,c=8
by cosine rule:
b^2=a^2+c^2-2ac*cosB
289=225+64-2*8*15*cosB
cosB=0
B=90

SO,eventualy the angle bisector of angle ABC will bisect AC
and the length of angle bisector will be=ac/a+b+c=(15*8)/(15+8+17)=3cm
So ...a/c to me correct answer is 3cm!

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Pratiksha Pandey  (7 years ago)

(ANS- 6.3) Here AB= 8(base), BC= 15(perpendicular) and AC= 17(hypotenuse), now angle bisector of ABC bisects AC into two parts (8.5 each). In New right angled triangle ABC', AB= 8, AC'= 8.5 and BC'= ?
(apply pythagorous theorm)

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Saikat Chakraborty  (7 years ago)

Its a rt. angled triangle from the (8 15 17) triplet. Now applying Apollonius' theorem 8^2+15^2=2(x^2+8.5^2) {x=angle bisector and 8.5 is half of side 17}

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