If sides of a triangle have lengths 8 ft and 12 ft.

Question

asked Aug 28, 2022 138k views

1 Answer

Barracel · Answer 1 · 2022-09-02T18:24:58+0000

Answer:

20 > c > 4

Explanation:

Given

$Sides =8\ and\ 12$

Required

The third side

To do this, we make use of the triangle inequality theorem which implies that:

a + b > c

a + c > b

b + c > a

Where

$a,b,c\to sides$

So, we have:

8 + 12 > c

8 + c > 12

12 + c > 8

Solve all inequalities

8 + 12 > c

20 > c

8 + c > 12

c > 4

12 + c > 8

c > -4

Ignore negative inequalities.

So, we have:

20 > c and
c > 4

Combine

20 > c > 4

The above implies that the third length is between 5 and 19 (inclusive)