Let's find the length of the other leg of the right triangle step-by-step.
We know the following:
- The length of one leg of the right triangle is 1 cm more than twice the length of the other leg.
- The length of the shortest leg is 6.8 cm.
- The hypotenuse of the triangle measures 16 cm.
### Step-by-Step Solution
1. Define Variables:
- Let [tex]\( a \)[/tex] be the length of the shortest leg.
- Let [tex]\( x \)[/tex] be the length of the other leg.
2. Establish the Relationship:
- According to the problem, the length of one leg is 1 cm more than twice the length of the other leg.
- Therefore, [tex]\( a = 2x + 1 \)[/tex].
3. Substitute Known Values:
- We are given that [tex]\( a = 6.8 \)[/tex] cm.
- Plug this into the relationship:
[tex]\[ 6.8 = 2x + 1 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = 6.8 - 1 \][/tex]
[tex]\[ 2x = 5.8 \][/tex]
[tex]\[ x = \frac{5.8}{2} \][/tex]
[tex]\[ x = 2.9 \][/tex]
Therefore, the length of the other leg is 2.9 cm.
So, completing the solution:
Part 2 of 2:
The length of the other leg is [tex]\( 2.9 \)[/tex] cm.
This completes our solution for the lengths of the legs of the right triangle.
