QQuestionMathematics
QuestionMathematics
What is the perimeter of triangle ABC?
| $\begin{aligned} & \mathrm{A} \\ & \mathrm{C} \end{aligned}$ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
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Answer
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Step 1: Identify the lengths of each side of the triangle.
Where $a$ and $b$ are the lengths of the legs adjacent to the right angle, and $c$ is the length of the hypotenuse.
The given triangle is a right triangle, and we are given the lengths of all three sides. Side AB is the hypotenuse with a length of 15 units, side BC has a length of 12 units, and side AC is the remaining side with a length that can be found using the Pythagorean theorem:
Step 2: Calculate the length of side AC.
\begin{aligned}
We are given that the length of side AB (the hypotenuse) is 15 units, and the length of side BC is 12 units. We can use the Pythagorean theorem to find the length of side AC: a^{2}+b^{2} &= c^{2} \ 12^{2}+ 15^{2} &= AC^{2} \ 144 + 225 &= AC^{2} \ 369 &= AC^{2} \ AC &= \sqrt{369} \ &\approx 19.24 \text{ units} \end{aligned}
Final Answer
The perimeter of triangle ABC is approximately 46.24 units.
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