Question

Alguém me ajuda no 16 por favor!?

Answer 1

$Sejam~a,b~e~c~essas ~medidas~ e~ A_{Prisma} =2(ab+ac+bc) ~\\temos~que:\\ \begin {cases}a+b+c=20\\a^2+b^2+c^2=152\end {cases}\\(a+b+c)^2=((a+b)+c)^2=(a+b)^2+2. (a+b).c+c^2=\\a^2+2ab+b^2+2ac+2bc+c^2=a^2+b^2+c^2+2 (ab+ac+bc)\\\Larged\boxed { (a+b+c)^2= a^2+b^2+c^2+2 (ab+ac+bc) }\\\\20^2=152 +2 (ab+ac+bc)\\400-152= A_{Prisma} \\\Larged\boxed{ A_{Prisma}=248cm^2 }$