Question

qual a área de um retângulo cujo o perímetro é 36 cm e a diferença entre os lados é de 10 cm
pfvv me ajudaaa

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Per\acute imetro~de~um~ret\hat angulo}\\\underline{\rm de~dimens\tilde oes~b~e~h}\\\sf p=2\cdot(b+h)\\\sf p\longrightarrow per\acute imetro\\\sf b\longrightarrow base\\\sf h\longrightarrow altura\\\underline{\rm \acute Area~do~ret\hat angulo~de~dimens\tilde oes~b~e~h}\\\sf A=b\cdot h\\\sf A\longrightarrow \acute area\\\sf \end{array}}$

$\Large\boxed{\begin{array}{l}\sf p=36~cm\\\sf 2\cdot(b+h)=36\\\sf b+h=\dfrac{36}{2}\\\sf b+h=18~cm\\\sf b-h=10\\\underline{\rm escrevendo~o~sistema~temos:}\\+\underline{\begin{cases}\sf b+\diagdown\!\!\!\!h=18\\\sf b-\diagdown\!\!\!\!h=10\end{cases}}\\\sf 2b=28\\\sf b=\dfrac{28}{2}\\\sf b=14~cm\\\sf b+h=18\\\sf 14+h=18\\\sf h=18-14\\\sf h=4~cm\end{array}}$

$\Large\boxed{\begin{array}{l}\sf A=b\cdot h\\\sf A=14\cdot 4\\\sf A=56~cm^2\end{array}}$