Question

Sardis was drawing a triangle. The first segment he drew was 10 centimeters. The 2nd side he drew was 12 centimeters. How long would the 3rd side have to be to create a triangle?
answer choices are
1 centimeter 24 centimeter 8 centimeters 2 centimeters

Answer 1

The third side can be of length 2 < x < 22

Step-by-step explanation:

• Let the third side be x
• Given two sides are 10, 12 cm respectively.
• According to Laws of Triangle

The sum of two sides should be greater than the third side.

⇒ 10 + 12 > x

⇒ 22 > x

The sum of two sides should be greater than the third side.

⇒ 10 + x > 12

⇒ x > 12 - 10

⇒ x > 2

(or)

The difference of two sides should be less than the third side.

⇒ 12 - 10 < x

⇒ 2 < x

The difference of two sides should be less than the third side.

⇒ x - 10 < 12

⇒ x < 12 + 10

⇒ x < 22

Therefore, The third side can be of length 2 < x < 22

Also learn more

Two sides of a triangle are 5 and 7 cm longer than the third side. If the perimeter is 21 cm , find the length of its side ?

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