Question

a carpenter is making a triangular frame for a garden trellis with three wooden beams. two of the beams are 15 feet and 10 feet long. the carpenter needs to cut a third beam to finish the frame. what could the length of the third beam be so that the frame makes a triangle? a 15.4 feet b 25 feet c 5 feet d 33.9 feet

Explanation:

Step1: Recall triangle inequality theorem

For a triangle with side lengths $a$, $b$, $c$, the sum of any two sides must be greater than the third side:

1. $a + b > c$
2. $a + c > b$
3. $b + c > a$

Step2: Define known and unknown sides

Let known sides $a=15$ ft, $b=10$ ft, unknown side $c$.

Step3: Find lower bound of $c$

Use $a - b < c$ (derived from $b + c > a$):
$15 - 10 < c$
$5 < c$

Step4: Find upper bound of $c$

Use $c < a + b$:
$c < 15 + 10$
$c < 25$

Step5: Check valid option

The valid range is $5 < c < 25$. Only 15.4 ft fits this range.

Answer:

A. 15.4 feet