Question

Type the correct answer in each box. Use numerals instead of words. An A-frame restaurant is shaped as a triangle with two side lengths of 20 m and 30 m. Complete the inequality below to describe the range of possible lengths x of the third side of the restaurant, ​

Answer 1

Answer:

• 10 < x < 50

Step-by-step explanation:

The triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side:

• x + 20 > 30  ⇒ x > 10
• x < 20 + 30 ⇒ x < 50
• x + 30 > 20, it is obvious for any positive x

The range of the value of x:

• 10 < x < 50

Answer 2

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We know that sum of two sides of a triangle should be always more than the third side , so

• $x < 20 + 30$
• $x < 50$

now, difference of measure of two sides of Triangle should be lower than that of third side :

• $x > 30 - 20$
• $x > 10$

now, by combining both the inequations, we get :

• $10 < x < 50$