Pregunta
In a right triangle, \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse. If \( a=2.9 \) units and \( b=0.7 \) units, what is the perimeter? If necessary, round your answer to the nearest tenth. units
Ask by Carrillo Mitchell. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The perimeter of the triangle is approximately 6.6 units.
Solución
Let the lengths of the legs be \( a = 2.9 \) and \( b = 0.7 \). The hypotenuse \( c \) is given by the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
1. Compute \( a^2 \) and \( b^2 \):
\[
a^2 = (2.9)^2 = 8.41,\qquad b^2 = (0.7)^2 = 0.49
\]
2. Find \( c \):
\[
c = \sqrt{8.41 + 0.49} = \sqrt{8.9} \approx 2.983
\]
3. Compute the perimeter \( P \):
\[
P = a + b + c = 2.9 + 0.7 + 2.983 \approx 6.583
\]
4. Round to the nearest tenth:
\[
P \approx 6.6 \text{ units}
\]
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Simplifique esta solución Extra Insights
To find the perimeter of the right triangle, you first need to calculate the length of the hypotenuse \( c \) using the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] Substituting the values of \( a \) and \( b \): \[ c = \sqrt{(2.9)^2 + (0.7)^2} = \sqrt{8.41 + 0.49} = \sqrt{8.9} \approx 2.983 \] Next, sum the lengths of the sides to find the perimeter \( P \): \[ P = a + b + c \approx 2.9 + 0.7 + 2.983 \approx 6.583 \] Rounding to the nearest tenth, the perimeter is approximately **6.6 units**.
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