Question

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

Answer 1

Answer:

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

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

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

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

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

⇒$\sf{ \frac{2w}{2} = \frac{142}{2} }$

Calculate

⇒$\sf{w = 71 \: m}$

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

$\boxed{ \sf{area \: of \: rectangle = l \times w}}$

plug the values

⇒$\sf{5185 = 61l}$

Swap the sides of the equation

⇒$\sf{61 \: l \: = 5185}$

Divide both sides of the equation by 61

⇒$\sf{ \frac{61 \: l}{61} = \frac{5185}{61} }$

Calculate

⇒$\sf{l = 85}$ cm

Length = 85 cm

Hope I helped!

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