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

See Explanation

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)`