Question

in a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. if $a = 5$ centimeters and $b = 5$ centimeters, what is the perimeter? if necessary, round to the nearest tenth. $square$ centimeters

Explanation:

Step1: Calculate hypotenuse length

Use Pythagorean theorem: $c = \sqrt{a^2 + b^2}$
Substitute $a=5$, $b=5$:
$c = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.071$

Step2: Calculate total perimeter

Sum all side lengths: $P = a + b + c$
Substitute values:
$P = 5 + 5 + 7.071 = 17.071$

Step3: Round to nearest tenth

Round $17.071$ to 1 decimal place: $17.1$

Answer:

17.1 centimeters