Answer:
a. [tex] \boxed{ \bold{ \boxed{ \sf{width \: of \: rectangular \: field \: = 71 \: meter}}}}[/tex]
b. [tex] \boxed{ \bold{ \boxed{ \sf{length \: of \: rectangular \: painting \: = 85 \: cm}}}}[/tex]
Step-by-step explanation:
a. Given,
Perimeter of rectangular field ( P ) = 310 m
Length of the field ( L ) = 84 m
Width of the field ( W ) = ?
Finding the width of the rectangular field
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}[/tex]
plug the values
⇒[tex] \sf{310 = 2(84 + w)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{310 = 168 + 2w}[/tex]
Swap the sides of the equation
⇒[tex] \sf{168 + 2w = 310}[/tex]
Move 168 to right hand side and change it's sign
⇒[tex] \sf{2w = 310 - 168}[/tex]
Subtract 168 from 310
⇒[tex] \sf{2w = 142}[/tex]
Divide both sides of the equation by 2
⇒[tex] \sf{ \frac{2w}{2} = \frac{142}{2} }[/tex]
Calculate
⇒[tex] \sf{w = 71 \: m}[/tex]
Width = 71 meters
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2. Given,
Area of rectangular painting ( A ) = 5185 cm²
Width of the painting ( w ) = 61 cm
Length of the painting ( l ) = ?
Finding length of the painting
[tex] \boxed{ \sf{area \: of \: rectangle = l \times w}}[/tex]
plug the values
⇒[tex] \sf{5185 = 61l}[/tex]
Swap the sides of the equation
⇒[tex] \sf{61 \: l \: = 5185}[/tex]
Divide both sides of the equation by 61
⇒[tex] \sf{ \frac{61 \: l}{61} = \frac{5185}{61} }[/tex]
Calculate
⇒[tex] \sf{l = 85}[/tex] cm
Length = 85 cm
Hope I helped!
Best regards !!!
