A soma dos comprimentos dos catetos de um triângulo retângulo?

Question

A soma dos comprimentos dos catetos de um triângulo retângulo cujos lados estão em progressão aritmética e cuja hipotenusa mede 10/3 cm é:
4, 14, 14/3, 13/3, 3?

Answer 1

os lados são 10/3 (hipotenusa sempre é o maior), 10/3-r e 10/3-2r
Usando o teorema de Pitágoras (o bom e velho Pitty) temos

(10/3)² = (10/3 - r)² + (10/3 - 2r)²
100/9 = 100/9 - 20r/3 + r² .+ 100/9 - 40r/3 + 4r²
100 = 100 - 60r + 9r² + 100 - 120r + 36r²
45r² - 180r + 100 = 0 simplificando por 5, temos
9r² - 36r + 20 = 0

delta = 1296 - 720 = 576
r = (36 +- 24)/18
r1 = 60/18 = 10/3
r2 = 12/18 = 2/3

10/3 não serve, pois se tirarmos 10/3 teremos cateto nulo.

Assim, os catetos são 8/3 e 6/3, cuja soma é 14/3

Answer 2

Before taking this medicine

Do not use Soma if you are allergic to carisoprodol or meprobamate (Equanil, Miltown), or if you have porphyria.
Before using Soma, tell your doctor if you are allergic to any drugs, or if you have:
- epilepsy or other seizure disorder;
- liver disease; or
- kidney disease.
If you have any of these conditions, you may need a dose adjustment or special tests to safely take Soma.
Soma may be habit-forming and should be used only by the person it was prescribed for. Soma should never be given to another person, especially someone who has a history of drug abuse or addiction. Keep the medication in a secure place where others cannot get to it. You may have withdrawal symptoms when you stop using Soma after using it over a long period of time. Withdrawal symptoms include stomach pain, sleep problems, headache, nausea, and seizure (convulsions). Do not stop using Soma suddenly without first talking to your doctor. You may need to use less and less before you stop the medication completely. Soma may be harmful to an unborn baby. Tell your doctor if you are pregnant or plan to become pregnant during treatment. It is not known whether Soma passes into breast milk or if it could harm a nursing baby. Do not use this medication without telling your doctor if you are breast-feeding a baby. Do not give this medication to a child younger than 12 years old..


Order Soma Online --> http://soma3.4gw.pw/w1kah

Answer 3

14/3

Answer 4

É simples:14/3