Question

in a right triangle, $a$ and $b$ are the lengths of the legs and $c$ is the length of the hypotenuse. if $a = 7$ kilometers and $c = 10$ kilometers, what is the perimeter? if necessary, round to the nearest tenth. $square$ kilometers

Explanation:

Step1: Calcular el cateto faltante

Usar el teorema de Pitágoras: $b = \sqrt{c^2 - a^2}$
Sustituir valores: $b = \sqrt{10^2 - 7^2} = \sqrt{100 - 49} = \sqrt{51} \approx 7.141$

Step2: Calcular el perímetro

Sumar los lados del triángulo: $P = a + b + c$
Sustituir valores: $P = 7 + 7.141 + 10 = 24.141$

Step3: Redondear al décimo más cercano

Redondear 24.141: $P \approx 24.1$

Answer:

24.1 kilómetros