Question

Determine a área de um retângulo sabendo q ele possue 32cm de perímetro e sua altura é 4cm menor que a base

Answer 1

$\large\boxed{\begin{array}{l}\sf Seja\,x\,o\,comprimento\,do\,ret\hat angulo\\\sf se\,a\,altura\,\acute e\,4\,cm\,a,\,menos\,que\,o\,comprimento\\\sf podemos\,represent\acute a-la\,por\,x-4.\\\sf Para\,calcular\,o\,per\acute imetro\,do\,ret\hat angulo\\\sf basta\,somar\,as\,dimens\tilde oes\,e\,multiplicar\,por\,2.\\\sf Portanto\\\sf P=2\cdot(x+x-4)\\\sf P=2\cdot(2x-4)=4x-8.\end{array}}$

$\large\boxed{\begin{array}{l}\sf O\,exerc\acute icio\,nos\,informa\,que\,o\,per\acute imetro\,\acute e\,32\,cm.\\\sf Podemos\,ent\tilde ao\,escrever:\\\sf 4x-8=32\\\sf 4x=32+8\\\sf 4x=40\\\sf x=\dfrac{40}{4}\\\\\sf x=10\,cm\\\sf para\,descobrir\,a\,altura,basta\,diminuir\,4.\\\sf portanto~h=10-4=6\\\sf A\,\acute area\,do\,ret\hat angulo\,\acute e\,dada\,por\\\sf A=x\cdot h\\\sf onde\,x\,\acute e\,o\,comprimento\,e\,h\,a\,altura.\\\sf A=10\cdot6\\\sf A=60\,cm^2\end{array}}$