Answer:
30 feet²
Step-by-step explanation:
Given: Length of rectangle is 4 times as it is wide.
Area of rectangle is 36 feet²
Lets assume the width of rectangle be "w"
∴ Length of the rectangle will be 4w.
Now, using the formula for Area of rectangle to know width and length of rectangle.
Formula; Area of rectangle= [tex]width\times length[/tex]
⇒ [tex]36= w\times 4w[/tex]
⇒ [tex]36= 4w^{2}[/tex]
Dividing both side by 4
⇒ [tex]\frac{36}{4} = w^{2}[/tex]
⇒[tex]9= w^{2}[/tex]
Taking square root on both side. remember; √a²=a or -a
⇒[tex]w=\sqrt{9}[/tex]
∴ [tex]w=3\ feet\ or -3\ feet, however, \ -3\ is\ ignored\ as\ length\ cannot\ be\ negative[/tex]
Next, subtituting the value of width to find legth of rectangle.
Length= [tex]4w[/tex]
∴ Length= [tex]4\times 3= 12\ feet[/tex]
Lets find the Perimeter of rectangle now.
Formula; Perimeter= [tex]2l+2w[/tex], where l = length and w= width
⇒ [tex]Perimeter = 2\times 12+2\times 3[/tex]
⇒ [tex]Perimeter= 24+6[/tex]
∴ Perimeter= [tex]30 feet^{2}[/tex]
Hence, perimeter of the rectangle is 30 feet²
