Latest Elitmus Aptitude Question SOLUTION: A square is inscribed in a triangle with side length 10,17 and 21 such that it touches the two side of the triangle and rests on the largest third side.Determine side of such a squ

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(#M40038038) ELITMUS Numerical Ability question Square and Triangle Keep an EYE

A square is inscribed in a triangle with side length 10,17 and 21 such that it touches the two side of the triangle and rests on the largest third side.Determine side of such a square.

Asked In Elitmus Vivek Jain (9 years ago)

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Liti  (9 years ago)

let the triangle is ABC,
a,b,c are sides ; AB=a=17, BC=b=21, CA=c=10
let the side of square is d

area of triangle= root{s(s-a)(s-b)(s-c)}=84

s=1/2(a+b+c)=48/2=24

area of triangle=1/2*height*base
1/2*21*height=84
so height=8

now we will get 2 congruent triangles,
and the smaller triangle will have
base= side of square=d, height= height of abc triangle-d=8-d


(height of ABC triangle) (height of ABC triangle)
------------------------- = -----------------
(base of ABC triangle) (base of ABC triangle)

8/21=(8-d)/d
d=168/29.

Is this solution Helpfull? Yes (31) | No (7)  

Mani Shankar  (9 years ago)

let the triangle is ABC,
a,b,c are sides ; AB=a=17, BC=b=21, CA=c=10
let the side of square is d

area of triangle= root{s(s-a)(s-b)(s-c)}=84

s=1/2(a+b+c)=48/2=24

area of triangle=1/2*height*base
1/2*21*height=84
so height=8

since this height is perpendicular to largest side on which square rests, so side of such square is 8

Is this solution Helpfull? Yes (1) | No (17)  

Brinder Singh  (9 years ago)

@B.Laxmi how can the name of both the triangles be same? may you please clear what is the name of the small triangle ur taking. .

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