The perimeter of a rectangle is 96ft. the ratio of the length to the width is 7: 5. what are the dimensions of the rectangle?

l = 28 ft; w = 20 ft

Step-by-step explanation:

We have two bits of information

(a) The perimeter of the rectangle

The formula for the perimeter of a rectangle is

              P = 2l + 2w

              P = 96 ft     Insert into the formula

(1) 2l + 2w = 96

(b) The length-to-width ratio

 l/w = 7/5     Multiply both sides by w

(2) l =(7w)/5

Substitute the value of l from Equation (2) into Equation (1)

2×(7w)/5 + 2w = 96

Solve for w

(14w)/5 + 2w = 96     Multiply each side by 5

  14w + 10w = 480    Combine like terms

           24w = 480    Divide each side by 24

               w = 20 ft

Solve for l

Substitute the value for w into Equation (1).

2l +2×20 = 96

   2l +40 = 96     Subtract 40 from each side

          2l = 56      Divide each side by 2

            l = 28 ft

The rectangle is 28 ft long and 20 ft wide.

Check:

P = 2×28 + 2×20  

P = 56 + 40

P = 96 ft

Also

l/w = 28/20

l/w = 7/5

idk

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900 degrees

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