Question

The three sides of a quadrilateral have lengths 10, 12 and 14. Between what values must the length of the fourth side lie?​

Answer 1

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Answer 2

The fourth side lie between 8 and 36.

The three sides of a quadrilateral have lengths 10, 12 and 14.

Between what values must the length of the fourth side lie ?

Let x be the fourth side of quadrilateral.

Here, a = 10, b = 12 and c = 14

• case 1 : a + b + c = 10 + 12 + 14 = 36 , It is the longest line segment using given sides of quadrilateral.
• case 1 : a + b - c = 10 + 12 - 14 = 8 , It is the smallest line segment using them.
• So the fourth side must be lie between 8 to 36.

Therefore the fourth side belongs to (8, 36).

i.e., 8 < x < 36 ⇒9 ≤ x ≤ 35

Total possible value of fourth side = (35 - 9) + 1 = 27

Therefore the fourth side lie between 8 and 36. and there are 27 values of it.