Question

16 Na figura, o triângulo ABC é semelhante ao triângulo DEF. Nessas condições, determine as medidas a e b assinaladas na figura. ​

Answer 1

$\Large\boxed{\begin{array}{l}\sf\triangle ABC\sim\triangle DE~\!\!F\\\sf\dfrac{10}{4}=\dfrac{16}{b}\\\\\sf 10b=64\\\sf b=\dfrac{64\div2}{10\div2}=\dfrac{32}{5}\\\\\sf 2a+b=16\\\sf 2a+\dfrac{32}{5}=16\bullet5\\\\\sf 10a+32=80\\\sf 10a=80-32\\\sf 10a=48\\\\\sf a=\dfrac{48\div2}{10\div2}\\\\\sf a=\dfrac{24}{5}\end{array}}$