Is the perimeter of a triangle greater than 30?

Is the perimeter of a triangle greater than 30?
a + b + c > 30 ? where a, b and c are side of triangle.

(1) The shortest side's length is greater than 10.
Let a be the shortest side. So a > 10.
Hence both b and c would be greater than 10 satisfying the condition b + c > a. So, b > 10 and c > 10
Adding the three sides thus gives a + b + c > 30 (Shortest perimeter would be for equilateral triangle whose sides are just greater than 10)

SUFFICIENT.

(2) The longest side's length is greater than 15.
Let c be the longest side. So, c > 15
So the condition for the triangle to form is that a + b > 15 where a and b are the other two sides.

Adding both
a + b + c > 30 (E.g. a = 1, b = 14.1 and c = 15.05 such that a + b + c = 30.15)

SUFFICIENT.

Answer D.

(1) The shortest side's length is greater than 10.
=> perimeter of a triangle greater than (10 + 10 + 10)
=> Suff

(2) The longest side's length is greater than 15.
The triangle inequality => total of the rest side's length of that triangle greater than 15
=> perimeter of a triangle greater than 30
=> Suff

=> Choice D

Is the perimeter of a triangle greater than 30?

(Statement1): The shortest side's length is greater than 10.
—>Even if all sides’ lengths are equal to one another, the least value of perimeter of a triangle will be greater than 30.
Sufficient

(Statement2): The longest side's length is greater than 15.
—> According to the features of a triangle, the length of one side must be less than the sum of the lengths of two other sides( a+b >c)
—> if c >15, the sum of the lengths of two other sides must be greater than 15 too. —> the perimeter should be greater than 30 —> a+b+c > 30.
Sufficient

The answer is D.

Posted from my mobile device

Is the perimeter of a triangle greater than 30?

(1) The shortest side's length is greater than 10.
So the other two sides are also greater than 10. Sufficient.

(2) The longest side's length is greater than 15.
So the sum of the other two sides are also greater than 15. Sufficient.

We are to determine if the perimeter of a triangle is greater than 30.

Statement 1: The shortest side's length is greater than 10.
This is sufficient since the remaining two sides will be more than 10, hence the perimeter will be more than 30.

(2) The longest side's length is greater than 15.
Sufficient since the sum of the remaining two sides will be more than 15 in order to form a triangle, hence the perimeter will be more than 30.

Both statements on their own are sufficient.

The answer is therefore D.

(1) The shortest side's length is greater than 10. sufic

ABC: B-A<C<B+A, C-A<B<C+A, C-B<A<C+B
ABC: 10.01,10.01,10.01 = 30.03

(2) The longest side's length is greater than 15. sufic

ABC: B-A<C<B+A, C-A<B<C+A, C-B<A<C+B
if C>15, and C-B<A<C+B, then 15.01<A+B, so C+A+B>30

Ans (D)

#1The shortest side's length is greater than 10.
So smallest side is 11 and other two sides must be at least 12 and 13
Sufficient
#2
The longest side's length is greater than 15.
Least other side can be 10 &7 as sum of 2 sides> third side.
Sufficient
IMOD

Is the perimeter of a triangle greater than 30?

(1) The shortest side's length is greater than 10.
(2) The longest side's length is greater than 15.

Posted from my mobile device

Is the perimeter of a triangle greater than 30?

(1) The shortest side's length is greater than 10.
(2) The longest side's length is greater than 15

The general rule for 3 sides of triangle is that the longest side won't be more than the sum of two short sides and no one side can be less than the difference of the other two sides. Keeping this in mind we can analyze the 2 statements like this:

1) The 3 sides of the triangle can be 10.5, 12, 15. or can be 12, 15, 18. so no single answer is possible. insufficient.

2) Since the longest side is greater than 15, the sum of the remaining sides will be more than 15. sufficient.

B is the answer imho.

Is the perimeter of a triangle greater than 30?

(1) The shortest side's length is greater than 10.
(2) The longest side's length is greater than 15.

Solution: From stmnt (1), As the shortest side is greater than 10, perimeter must be greater than 30.

From statement (2), Longest could be 15.001, 16, ......... so so
Other two sides could be 1 and 2 or 14 and 15.
So perimeter of the triangle may be less than 30 or greater than 30
Ans.A

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