Question

The length of two sides of triangle are 4cm and 5cm. Between what two

Answer 1

Answer:

1 and 9

Step-by-step explanation:

By the Triangle Inequality Theorem, the sum of two side lengths of a triangle is always greater than the length of the third side.

In other words, in a triangle with side lengths $a, b,$ and $c,$ we always have $a+b > c.$

Applying this to this question, the other side length, $x,$ must satisfy the following inequalities:

$4+5 > x,\\x+5 > 4,\\x+4 > 5.$

Solving these inequalities gives

$x < 9,\\x > -1,\\x > 1.$

Combining these solutions, we have $1 < x < 9.$ Therefore, the length of the third side falls between 1 and 9.