Two sides of a triangle have lengths of 5 centimeters and 9 centimeters. Which of the foll… — GRE General Test

Two sides of a triangle have lengths of $5$ centimeters and $9$ centimeters. Which of the following could be the length, in centimeters, of the third side? Select all such lengths.

A
$4$
$6$ Cevap
$10$ Cevap
D
$14$
E
$16$

Cevap

The possible lengths for the third side are

6

centimeters and

10

centimeters.

According to the Triangle Inequality Theorem, the length of the third side

x

must be strictly greater than the difference of the two given sides (

9 - 5 = 4

) and strictly less than their sum (

9 + 5 = 14

). This establishes the valid range as

4 < x < 14

. The options

6

centimeters and

10

centimeters are the only values provided that fall strictly within this interval.

Adım Adım Çözüm

Apply the Triangle Inequality Theorem to determine the allowable range for the third side.

The length of the third side,

x

, must satisfy

|9 - 5| < x < 9 + 5

, which simplifies to

4 < x < 14

The sum of the lengths of any two sides of a non-degenerate triangle must be strictly greater than the length of the remaining side.

Check each candidate option against the inequality

4 < x < 14

The values

6

and

10

satisfy

4 < x < 14

, whereas

4

14

, and

16

do not.

Only numbers strictly within the open interval

(4, 14)

can form a valid triangle with side lengths

5

and

9

Anahtar Kavram

Triangle Inequality Theorem

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru