Question

Um retângulo tem area de 18m² e perímetro de 17m .quanto medem seus lados

Answer 1

b*h=18
b=18/h
2b+2h=17

$b= \frac{18}{h} \\\\ 2b+2h=17\\ 2* \frac{18}{h} +2h=17 \\\\ \frac{36}{h} +2h=17\\\\ 36+2h^2=17h\\ Reorganizando\\ 2h^2-17h+36=0$

$2h^2-17h+36=0\\\\ x_{1}= \frac{-(-17)+ \sqrt{17^2-4*2*36}}{4} \\\\ x_{1}= \frac{17+ \sqrt{17^2-4*2*36}}{4} \\\\ x_{1}= \frac{17+ \sqrt{289-288}}{4} \\\\ x_{1}= \frac{17+ \sqrt{1}}{4} \\\\ x_{1}= \frac{17+ 1}{4} \\\\ x_{1}= \frac{18}{4} \\\\ x_{1}= 4,5$

$2h^2-17h+36=0\\\\ x_{2}= \frac{-(-17)- \sqrt{17^2-4*2*36}}{4} \\\\ x_{2}= \frac{17- \sqrt{17^2-4*2*36}}{4} \\\\ x_{2}= \frac{17- \sqrt{289-288}}{4} \\\\ x_{2}= \frac{17- \sqrt{1}}{4} \\\\ x_{2}= \frac{17- 1}{4} \\\\ x_{2}= \frac{16}{4} \\\\ x_{2}= 4$

A base e a altura é 4 e 4,5.

$4*4,5=18 \\ e\\ 2*4+2*4,5=17$

Answer 2

A resposta é 4 e 4,5.