Question

(a) The perimeter of a rectangular field is 310 m.

If the length of the field is 84 m, what is its width?

(b) The area of a rectangular painting is 5185 cm.
If the width of the painting is 61 cm, what is its length?

Answer 1

a.
`\boxed{ \bold{ \boxed{ \sf{width \: of \: rectangular \: field \: = 71 \: meter}}}}`

b.
`\boxed{ \bold{ \boxed{ \sf{length \: of \: rectangular \: painting \: = 85 \: cm}}}}`

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

`\boxed{ \sf{perimeter \: of \: rectangle = 2(l + w)}}`

plug the values

⇒
`\sf{310 = 2(84 + w)}`

Distribute 2 through the parentheses

⇒
`\sf{310 = 168 + 2w}`

Swap the sides of the equation

⇒
`\sf{168 + 2w = 310}`

Move 168 to right hand side and change it's sign

⇒
`\sf{2w = 310 - 168}`

Subtract 168 from 310

⇒
`\sf{2w = 142}`

Divide both sides of the equation by 2

⇒
`\sf{ (2w)/(2) = (142)/(2) }`

Calculate

⇒
`\sf{w = 71 \: m}`

Width = 71 meters

------------------------------------------------------------

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

`\boxed{ \sf{area \: of \: rectangle = l * w}}`

plug the values

⇒
`\sf{5185 = 61l}`

Swap the sides of the equation

⇒
`\sf{61 \: l \: = 5185}`

Divide both sides of the equation by 61

⇒
`\sf{ (61 \: l)/(61) = (5185)/(61) }`

Calculate

⇒
`\sf{l = 85}` cm

Length = 85 cm

Hope I helped!

Best regards !!!