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A triangle has sides measuring 7 cm and 12 cm. Which of the
[#permalink]
22 Sep 2020, 04:52

Expert Reply

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Question Stats:

A triangle has sides measuring 7 cm and 12 cm. Which of the following are possible values for the perimeter of the triangle?

Indicate all possible values.

A. 22 cm

B. 24 cm

C. 26 cm

D. 28 cm

E. 30 cm

F. 34 cm

G. 38 cm

_________________

Indicate all possible values.

A. 22 cm

B. 24 cm

C. 26 cm

D. 28 cm

E. 30 cm

F. 34 cm

G. 38 cm

_________________

Re: A triangle has sides measuring 7 cm and 12 cm. Which of the
[#permalink]
22 Sep 2020, 05:09

1

1

Bookmarks

Carcass wrote:

A triangle has sides measuring 7 cm and 12 cm. Which of the following are possible values for the perimeter of the triangle?

Indicate all possible values.

A. 22 cm

B. 24 cm

C. 26 cm

D. 28 cm

E. 30 cm

F. 34 cm

G. 38 cm

Indicate all possible values.

A. 22 cm

B. 24 cm

C. 26 cm

D. 28 cm

E. 30 cm

F. 34 cm

G. 38 cm

IMPORTANT RULE: If two sides of a triangle have lengths A and B, then . . .

DIFFERENCE between A and B < length of third side < SUM of A and B

Since the two known sides have lengths 7 and 12, we can write: 12 - 7 < length of third side < 12 + 7

Simplify to get: 5 < length of third side < 19

IF the length of the third side were 5, then the perimeter would equal 7 + 12 + 5 = 24

However, since the length of the third side must be greater than 5, the perimeter must be greater than 24

Likewise, IF the length of the third side were 19, then the perimeter would equal 7 + 12 + 19 = 38

However, since the length of the third side must be less than 5, the perimeter must be less than 38

When we combine both pieces of information we get: 24 < perimeter < 38

The answer choices that work with us in equality are C, D, E and F

Answer: C, D, E, F

_________________

Re: A triangle has sides measuring 7 cm and 12 cm. Which of the
[#permalink]
28 Oct 2020, 02:02

1

3rd side should be < than the sum of other two sides - 19cm => perimeter should be less than 38 (7+12+19-)

3rd side should be > that the difference of other two sides - 5cm => perimeter should be greater than 24 (7+12+5+)

So, pick all values that satisfy 24<perimeter<38

3rd side should be > that the difference of other two sides - 5cm => perimeter should be greater than 24 (7+12+5+)

So, pick all values that satisfy 24<perimeter<38

Re: A triangle has sides measuring 7 cm and 12 cm. Which of the
[#permalink]
22 Aug 2023, 06:52

1

difference of other 2 sides < Length of 3rd side of a triangle < sum of other 2 sides

5 < Length of 3rd side of a triangle < 19

24 <perimeter < 38

5 < Length of 3rd side of a triangle < 19

24 <perimeter < 38

gmatclubot

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