Question

A field is a rectangle with a perimeter of 1160 feet. The length is 400 feet more than the width. Find the width and length of the rectangular field.

Answer 1

w = 90 feet and l = 490 feet

Explanation:

First, determine what you're given:

Perimeter = 1,160 feet

Perimeter = 1,160 feetlength = (w)idth + 400

idth + 400width = w

Next, solve for the length and the width using the perimeter equation (2l + 2w = Perimeter)

2(400+w) + 2w = 1,160 feet

(800 + 2w) + 2w = 1,160 feet

800 + 2w + 2w = 1,160 feet

800 + 4w = 1,160 feet

{ Subtract 800 from both sides }

4w = 360 feet

{ Divide both sides by 4 to isolate w }

w = 90 feet

Finally, you've solved for the width which is 90 feet. Plug this back into your equation for length;

[ l = 400 + w ]

l = 400 + (90)

l = 490 feet

Since it never hurts to check;

2l + 2w = 1,160 feet

2(400+w) + 2w = 1,160 feet

2(400+90) + 2w = 1,160 feet

✅2(490) + 2(90) = 1,160 feet