Question

(SAT Prep) If the lengths of two sides of a triangle measure 8 and 13 what could the length of the third side measure
(A) 6

(B) 21

(C) 3

(D) 4
Hint its not D.

Answer 1

Answer:

A)6

Step-by-step explanation:

Use the triangle inequality theorem, which states that the third side of a triangle can not be greater than or equal to the sum of the other two sides, and can be no less than the or equal to the difference of the two other sides.

The sum is 8+13=21

The difference is 13-8=5

So if we call our third side x, then

[tex]5

Answer 2

If the lengths of two sides of a triangle measure 8 and 13 units, using triangle inequality theorem, the length of the third side could be 6 units.

What is triangle inequality theorem?

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Given the two sides be 8 and 13 units.

Let the third side be x units.

First,

8 + 13 > x

21 > x

x < 21

Second,

8 + x > 13

x > 5

Third,

13 + x > 8

True for all values of x.

So,

5 < x < 21

From the given options, only 6 satisfies our condition.

Learn more about triangle inequality theorem here

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