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Whitepunk [10]
3 years ago
13

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

Mathematics
2 answers:
Helga [31]3 years ago
8 0
D
the answer is D because it is equilateral triangle
8090 [49]3 years ago
3 0

Answer:

B. 10 cm, 15 cm, 24 cm

Step-by-step explanation:

we know that

The <u>Triangle Inequality Theorem</u>, 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

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