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In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 3.3 kilometers and c = 5 kilometers, what is the perimeter? If necessary,
round to the nearest tenth.
kilometers
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Verified Answer :

GinnyAnswer

Of course! Let's solve this step-by-step.

1. Understand the Problem:
We have a right triangle where:
- \(\( b = 3.3 \)\) kilometers (one leg)
- \(\( c = 5 \)\) kilometers (the hypotenuse)

2. Use the Pythagorean Theorem:
The Pythagorean theorem states that for a right triangle:
\(\[ a^2 + b^2 = c^2 \]\)

3. Rearrange to Solve for \(\( a^2 \)\):
Substitute in the given values \(\( b = 3.3 \)\) and \(\( c = 5 \)\):
\(\[ a^2 + 3.3^2 = 5^2 \]\)
\(\[ a^2 + 10.89 = 25 \]\)

4. Solve for \(\( a^2 \)\):
\(\[ a^2 = 25 - 10.89 \]\)
\(\[ a^2 = 14.11 \]\)

5. Find \(\( a \)\):
Take the square root of both sides to find \(\( a \)\):
\(\[ a = \sqrt{14.11} \]\)
\(\[ a \approx 3.75 \]\)

6. Calculate the Perimeter:
The perimeter \(\( P \)\) of a triangle is the sum of all its sides:
\(\[ P = a + b + c \]\)

Substitute \(\( a \approx 3.75 \)\), \(\( b = 3.3 \)\), and \(\( c = 5 \)\):
\(\[ P = 3.75 + 3.3 + 5 \]\)
\(\[ P = 12.05 \]\)

7. Round to the Nearest Tenth:
Therefore, rounding \(\( 12.05 \)\) to the nearest tenth:
\(\[ P \approx 12.1 \]\)

Final Answer:
The perimeter of the right triangle is approximately \(\( 12.1 \)\) kilometers.

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