Latest Elitmus Aptitude Question SOLUTION: A triangle having sides 10, 17 , 21 . A square is placed inside the triangle touching two sides and lie on the largest side of a triangle. Find the length of square?

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A triangle having sides 10, 17 , 21 . A square is placed inside the triangle touching two sides and lie on the largest side of a triangle. Find the length of square?

Asked In Elitmus Narendra Pargain (10 years ago)

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rohit tandon  (10 years ago)

m sry answer is 168/29......apply Heron's formula get the area ,equate the area with 0.5*b*h to get h (altitude),h=8, and then by basic proportionality theorem we get length of the square= 168/29.

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rohan chawla  (10 years ago)

length of square is 168/29 units

let us consider a triangle abc with ab = 10, bc=21 and ac =17
let square be pqrs with points p on ab, q and r on bc and s on ac
let each side of square is x. we have to find x
now for this we apply cosine formula in triangle abc to get angle b and c
cos(ang b)= 0.6
cos(ang c)= 15/17

now we see smaller triangles pbq and src
in triangle pbq
cos(ang b) = 0.6 so sin(ang b) = 0.8
tan (ang b)= 4/3 = pq/qb
pq=x
so x/qb = 4/3
qb = 3/4x

now seeing in triangle src
cos(ang c)= 15/17
tan(ang c)= 8/15
sr/rc = tan(ang c) =8/15
sr = x


now bc=21 = qb+qr+rc
qr=x (as it is side of square)
qb= 3/4x
rc = bc-(qr+qb) = 21-7/4x

now sr/rc=8/15
x/(21-7/4x) = 8/15
solving we get x = 168/29

Is this solution Helpfull? Yes (4) | No (1)  

Mr. Hmp  (10 years ago)

awesome problem... see this it will help http://www.qbyte.org/puzzles/p076s.html

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swati ahuja  (10 years ago)

base of triangle=b=21 and height=h,square side=x.
find area by heron's formula and equate it to 0.5*b*h..get the h
The area of the whole triangle is b*h/2.
The area of the small triangle on the top is x*(h-x)/2
The area of the square is x^2.
The area of the triangle that is obtained by sliding together the two smaller triangles standing on the base is (b-x)*x/2.
So
x = b*h/(b + h).

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Amardip Gautam  (10 years ago)

Ans -> 5.6
-> base of triangle=b=21 and height=h,square side=a.
-> find area by heron's formula(=84)and equate it to 0.5*b*h..get the h = 8.
-> The area of the whole triangle =(The area of the small triangle on the top) + (The area of the triangle that is obtained by sliding together the two smaller triangles standing on the base) + area of square
=>84 = [a*(h-a)/2] + [(b-a)*a/2] + a^2.
=>84 = [a*(8-a)/2] + [(21-a)*a/2] + a^2.
=>solving, a = 5.6

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rohit tandon  (10 years ago)

length of square would be 7 units.

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ranjeet singh chauhan  (10 years ago)

Asan question hai,, but i passed it. Due to lack of time.

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Priyansh   (10 years ago)

http://www.qbyte.org/puzzles/p076s.html

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