Latest Elitmus Aptitude Question SOLUTION: A square of the longest possible side is drawn inside the triangle ABC with one side of the square lying on side BC. If AB = 13, BC = 21 and AC = 20, find the side of the square.

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(#M40038468) ELITMUS Numerical Ability question geometry Keep an EYE

A square of the longest possible side is drawn inside the triangle ABC with one side of the square lying on side BC. If AB = 13, BC = 21 and AC = 20, find the side of the square.
A.84/11
B.7
C.28/3
D.31/4

Asked In Elitmus T.VIGNESWARA REDDY (9 years ago)

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RAKESH  (9 years ago)

A. 84/11

s=(13+21+20)/2 = 27

Area of triangle(A)= [27*(27-13)*(27-21)*(27-20)]^(.5) = 126

height of triangle(h)= 2*A / base = 2*126/21 = 12

from, similarity of triangles

h/(h-x) = BC / x where x is side of square
=> 12/(12-x) = 21/x
=> x = 84/11

Is this solution Helpfull? Yes (55) | No (1)  

Kolluru Nagalakshmi  (9 years ago)

a Square contain equal length of side,there is no longest size or shortest size.
he give square side BC=21,this is length of all sides

Is this solution Helpfull? Yes (1) | No (11)  

akash verma  (9 years ago)

DEFG SQUARE

triangle ABC and triangle ADE

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jyotshna bhardwaj  (8 years ago)

Let P and Q are the vertices of the square on AB and AC respectively and R and S on side BC.
s=(13+21+20)/2 = 27

Area of triangle(A)= [27*(27-13)*(27-21)*(27-20)]^(.5) = 126

height of triangle(h)= 2*A / base = 2*126/21 = 12
now from, similarity of triangles APQ and ABC
12-X/21=X/12
X=48/11

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ak  (9 years ago)

@ rakesh
kindly explain h/(h-x) = BC / x where x is side of square,
which 2 triangles you have taken as similar..

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