perimeter of triangle=48,and one side 14 units.if sides are integer then wha is the smaller length of other two sides

Question

explain in detail sir and short trick for GRE

Answer 1

Using the side formula and calling the sides a, b, c

 

s = (sum of all sides)/2 = perimeter/2 = 48/2 = 24

 

Area = square root of s(s-a)(s-b)(s-c)

 

c = 14

 

a + b = 48 - 14 = 34

 

==> b = 34 - a

 

now substitute all the new values

 

in to the square root 24(24-a)(24-(34-a)(24-14)

 

Rewrite

 

24(24-a)(-10+a)(24-14)

 

 

You can see that a has to be greater than 10

 

if we allow a to be ten we get 24 for b

 

==> that a is the smallest and hence the one to be adjusted to the nearest integer which is 11

 

 

 

Answer 2

The perimeter of a triangle is the sum of the lengths of the three sides.

 

x + y + 14 = 48

x + y = 34

 

So the other two sides could any lengths that add to 34.