Question

The lengths of two sides of a triangle are 26
meters and 48 meters. What is the range of
possible lengths, in meters, for the third side,
x, of this triangle? Write your answers in the
boxes.

Answer 1

Answer:

$22\ m < x < 74\ m$

Step-by-step explanation:

Let

x ----> the length for the third side

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Applying the triangle inequality theorem

1) $26+48> x$

solve for x

$74> x$

Rewrite

$x < 74\ m$

2) $26+x>48$

solve for x

subtract 26 both sides

$x> 22\ m$

therefore

The range of  possible lengths, in meters, for the third side is equal to

$22\ m < x < 74\ m$

Answer 2

The range of the possible length of the third side of the triangle is 22 to 74 (exclusive)

Assume the lengths of a triangle are x, y and z.

The following are the possible inequalities that relate the side lengths

$x + y > z$

$y + z > x$

$x + z > y$

The unknown side length is x.

So, we have:

$x + 26 > 48$

$48 + 26 > x$

$x + 48 > 26$

Solve for x in the three inequalities

$x + 26 > 48$

$x > 22$

$48 + 26 > x$

$74 > x$

$x + 48 > 26$

$x > -22$

The values of x cannot be negative.

So, we ignore the inequality $x > -22$

We are left with

$74 > x$ and $x > 22$

Combine the inequalities

$74 > x > 22$

Rewrite as:

$22 < x < 74$

Hence, the range of the possible length is 22 to 74 (exclusive)

Read more about triangle inequalities at:

https://brainly.com/question/18284285