What is the length of a rectangle with the perimeter of 56 if the width is 4 inches greater than 1/2 the length

Answer 1

Hi, Darla!

Call the width of the rectangle W and call the length of the rectangle L. The perimeter is the distance around all sides of the rectangle, or 2W + 2L. Since we know that the perimeter of the rectangle is 56, we know that 2W + 2L = 56. We also know that the width of the rectangle is half of the length plus 4 inches, therefore W = 1/2L + 4.

2W + 2L = 56

2(1/2L + 4) +2L = 56

L + 8 + 2L = 56

3L + 8 = 56

3L = 48

L = 16

We’ve found that the length of the rectangle is 16 inches. Let’s check our answer. The width, W = 1/2L + 4 so W = 1/2*16 + 4 so W= 8 + 4 = 12. Remember that the perimeter of the rectangle is 2W + 2L. The perimeter is 2L + 2W = 2*16 + 2*12 = 32 + 24 = 56 so we know our answer is correct!😊

Answer 2

p=56= 2(w+L)

w+L = 28

w=4+L/2

4+.5L+L = 28

1.5L = 28-4=24

L = 24/1.5 = 8/.5 = 16 inches Long

w = 4+8 = 12 inches wide

2(16+12) = 2(28) =56 inches = the Perimeter

Answer 3

Hi Darla,

You have a rectangle with perimeter, P, length, L and width, W. P = 2L + 2W for a rectangle.

"If the width is 4 inches greater than 1/2 the length" means: W = 4 + (1/2)*L.

Substitute that equation for W into P = 2L + 2W.

This gives: P = 2L + 2(4 + (1/2)*L) = 2L + (2*4) + (2*(1/2))L = 2L + 8 + L = 3L + 8.

P = 56 inches = 3L + 8. Subtract 8 from both sides: 3L = 48 so L = 16 inches.

You should always doublecheck your answer! This means, if you plug in L = 16 to these equations, P should equal 56!

Let's see: L = 16. W = 4 + (1/2)*L = 4 + (1/2)*(16) = 4 + 8 = 12. So, W = 12.

P = 2L + 2W = 2(16) + 2(12) = 32 + 24 = 56! So, L does = 16 inches.

Answer 4

L/2 + 4 = W; 2L + 2W = 56; W = 28 - L; L/2 + 4 = 28 - L; 3L/2 = 24; L = 16 inches