Latest NTSE Aptitude Question SOLUTION: The length of the sides of a triangle are in integers and its area >is also an integer. One side is 21 cm and the perimeter is 48 cm, >then the length of the shortest side is :

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(#M40003598) NTSE General Ability question Finding the shortest side of a triangle Keep an EYE

The length of the sides of a triangle are in integers and its area
>is also an integer. One side is 21 cm and the perimeter is 48 cm,
>then the length of the shortest side is :

Asked In NTSE Sanjana Patnaik (13 years ago)

Unsolved Read Solution (4)

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kiran kumar reddy  (13 years ago)

ans:84

Sum of other 2 sides = 27.
=> If one side = x, other = 27 - x.
Using Heron's formula,
=> A^2 = 24*3*(24-x)*(x-3)
RHS must be a perfect square
=> A^2 = 6^2 * 2 * (24-x)(x-3) is a perfect square
=> x = 10, Other side = 17
=> shortest side = 10 cm.
Other sides are 17 and 21 cm,
Area = 84 sq cm.

Is this solution Helpfull? Yes (11) | No (4)  

Dr.Dipin Singh  (13 years ago)

shortest side is 10 cms.

all 3 sides are 10,17,21 cms.

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venkatesh  (9 years ago)

The length of the sides of a triangle are in integers and its area
>is also an integer. One side is 21 cm and the perimeter is 48 cm,
>then the length of the shortest side is :
Read more at http://www.m4maths.com/3598-The-length-of-the-sides-of-a-triangle-are-in-integers-and-its-area-is-also-an-integer-One-side.html#OXJQs7r9Ml1C1KKA.99

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venkatesh  (9 years ago)

The length of the sides of a triangle are in integers and its area
>is also an integer. One side is 21 cm and the perimeter is 48 cm,
>then the length of the shortest side is :
Read more at http://www.m4maths.com/3598-The-length-of-the-sides-of-a-triangle-are-in-integers-and-its-area-is-also-an-integer-One-side.html#oVaQlqv3VGR9vOEG.99

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