Question

The length of a rectangle is six times its width.

If the perimeter of the rectangle is
98

yd
, find its area.

Answer 1

Alright, so we'll be playing a little with variables around here. The question tells you the length of a rectangle is six times its width, or that l=6w.

The perimeter of a rectangle is 2l + 2w (two times the length + two times the width). Since we established that l=6w...

2(6w) + 2w = 98 yd
12w + 2w = 98 yd
14w=98 yd
w=7 yd.

But it doesn't stop there. We found that the width is 7 yd. So the length is 6w, or 6 x 7 yd, which is 42 yd. To find the area of a rectangle, you multiply the length by the width.

So...42 yd x 7 yd = 294 yd^2.

Hope that helped.

Answer 2

The width of the rectangle is 7 yards and the length is 42 yards. The area of this rectangle is 294 square yards.

Step-by-step explanation:

This is a problem involving algebra and geometry. We are given that the length of a rectangle is six times its width. To represent this algebraically, if the width of the rectangle is w, then the length is 6w.

The perimeter of a rectangle is calculated by adding up all its sides, thus it is given by the formula 2 * (length + width). We know from the problem that the perimeter is 98 yards, so we can set up the equation 2 * (6w + w) = 98 to solve for w.

Upon solving, we find that w = 7 and thus, length = 6w = 42. Finally, the area of a rectangle is calculated by multiplying the length and the width, so the area is 42 * 7 = 294 square yards.

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