Question

Which three lengths could be the lengths of the sides of a triangle?

Answer 1

D
the answer is D because it is equilateral triangle

Answer 2

Answer:

B. $10$ cm, $15$ cm, $24$ cm

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of two sides of a triangle must always be greater than the length of the third side

so

$a+b > c$

$a+c > b$

$b+c >a$

where

a,b,c are the lengths sides of the triangle

case A)  $6$ cm, $23$ cm, $11$ cm

Let

$a=6\ cm$

$b=23\ cm$

$c=11\ cm$

Verify

$a+b > c$ ------> $6+23 > 11$ ------> is true

$a+c > b$ ------> $6+11 > 23$ -------> is not true

therefore

The three lengths of case A) could not be the lengths of the sides of a triangle

case B)  $10$ cm, $15$ cm, $24$ cm

Let

$a=10\ cm$

$b=15\ cm$

$c=24\ cm$

Verify

$a+b > c$ ------> $10+15 > 24$ ------> is true

$a+c > b$ ------> $10+24 > 15$ -------> is true

$b+c >a$ -----> $15+24 >10$ --------> is true

therefore

The three lengths of case B) could be the lengths of the sides of a triangle

case C)  $22$ cm, $6$ cm, $6$ cm

Let

$a=22\ cm$

$b=6\ cm$

$c=6\ cm$

Verify

$a+b > c$ ------> $22+6 > 6$ ------> is true

$a+c > b$ ------> $22+6> 6$ -------> is true

$b+c >a$ -----> $6+6 >22$ --------> is not true

therefore

The three lengths of case C) could not be the lengths of the sides of a triangle

case D)  $15$ cm, $9$ cm, $24$ cm

Let

$a=15\ cm$

$b=9\ cm$

$c=24\ cm$

Verify

$a+b > c$ ------> $15+9 > 24$ ------> is not true

therefore

The three lengths of case D) could not be the lengths of the sides of a triangle