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the maximum perimeter

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by sanju09 » Tue Oct 18, 2011 4:56 am
Given integers as the lengths of the sides of a triangle, what is the maximum perimeter of a triangle where two of the sides measure 10 and 14?
(A) 27
(B) 28
(C) 47
(D) 48
(E) 52
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by Anurag@Gurome » Tue Oct 18, 2011 5:00 am
sanju09 wrote:Given integers as the lengths of the sides of a triangle, what is the maximum perimeter of a triangle where two of the sides measure 10 and 14?
As the length of two of the sides of the triangles are 10 and 14 units, the length of the third side must be less than (10 + 14) = 24

The largest integer smaller than 24 is 23.
Hence, maximum perimeter the triangle can have = (10 + 14 + 23) = 47

The correct answer is C.
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by neelgandham » Wed Oct 19, 2011 3:59 am
Given integers as the lengths of the sides of a triangle, what is the maximum perimeter of a triangle where two of the sides measure 10 and 14?

Sum of two sides of a triangle is always greater than the third side.

say, x is the third side

10 + 14 > x => x < 24 ( 23, 22, ....)
10 + x > 14 => x > 4 ( 5, 6, 7, ...)
14 + x > 10 => x > -4 (-3, -2, -1....)

From the above in-equations, the maximum value of the third side = 23. Hence, the maximum perimeter = 14+10+x = 47, option C
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