caitlinjohnson2704
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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, ​

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mhanifa

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
DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

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

  • [tex]x < 20 + 30[/tex]
  • [tex]x < 50[/tex]

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

  • [tex]x > 30 - 20[/tex]
  • [tex]x > 10[/tex]

now, by combining both the inequations, we get :

  • [tex]10 < x < 50[/tex]

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