Question

The perimeter of a rectangle is 58 im with a length of 20 in.What is the area of the rectangle

Answer 1

Step1: Write out the given information

`\begin{gathered} \text{perimeter}=58in \\ \text{length}=20\text{ in } \end{gathered}`

Step2: write out the formula

`\text{perimeter}=2(l+w)`

Step3: Substitute the value and find the width of the rectangle

`\begin{gathered} 58=2(20+w) \\ \text{divide both sides by 2} \\ (58)/(2)=(2(20+w))/(2) \\ 29=20+w \\ \end{gathered}`

Then

`\begin{gathered} \text{subtract 20 from both sides } \\ 29-20=20-20+w \\ 9=w \\ \text{Hence, the width is 9 in} \end{gathered}`

Step4: Calculate the Area of the Rectangle

`\begin{gathered} \text{Area of rectangle =l}* w \\ \text{where l=20 and w=9} \\ \text{substitute the value } \\ \text{Area =20}*9 \\ \text{Area}=180in^2 \end{gathered}`

Therefore the Area of the rectangle is 180 in²