Question

HELP!!!

Define a variable, write an equation and solve your equation to find the answer to the following question.

Hagrid plans to put up new fencing around his rectangular garden. He wants the width of his new garden to be 6 less than the length. The perimeter of the new garden will be 188 feet. Create and use an algebraic equation to find the dimensions (length and width) of Hagrid's new garden. Show your work!

Answer 1

We can define variable as any factor, trait, or condition that can exist to vary or change.

Perimeter of rectangle = 2(l+w)
let l is the length of the garden
and w is the width of the garden = 6 less than the length = l - 6
perimeter = 188 feet
p = 2(l+w)
188 = 2 (l + (l-6))
188 = 2(l + l - 6)
188 = 2(2l-6)
188 = 4l - 12
4l = 188+12
4l = 200
l=50 
w = l - 6 = 50 - 6 = 44
Thus, the dimensions, length is 50 feet and width is 44 feet.

Answer 2

Let L = length. Therefore, by given information the width, W, is equal to L-6. Perimeter = 2*length + 2*width or 2L+2W. Substitute in values we get 188 = 2*L + 2*(L-6) Expand: 188 = 2*L + 2*L - 12 Add 12 to both sides and combine like terms: 200 = 4*L Divide both sides by 4: 50 = L The length if found to be 50 feet. The width is then 50 - 6, or 44 feet. We can confirm that the perimeter is 50+50+44+44 feet, or 188 feet.