Question

An architect is constructing a model in the shape of a triangle that has one side length of 9 centimeters and another side length of 8 centimeters. Which

Answer 1

Answer:

See Explanation

Step-by-step explanation:

Given

$Sides:\ 9cm\ and\ 8cm$

The question is incomplete, as what is required is not state. However, a possible question could be to determine the possible side length of the third side.

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

Given three sides (a, b and c) of a triangle, the following inequalities exist.

$a + b > c$

$a + c > b$

$b + c > a$

Let a and b represent the two sides such that:

$a = 9$

$b = 8$

The inequalities become:

$9 + 8 > c$

$9 + c > 8$

$8 + c > 9$

Solve for c in each:

$9 + 8 > c$

$17 > c$

$c < 17$

$9 + c > 8$

$c > 8 - 9$

$c > - 1$

$8 + c > 9$

$c >9 - 8$

$c >1$

The value of c must be positive, so, we consider;

$c >1$ and $c < 17$

Rewrite:

$1 < c$ and $c < 17$

Combine both

$1 < c < 17$

Hence, the value of c is:

$c = (1,17)$