Final answer:
The area of the rectangle is 600 square yards. To find the area of the rectangle, first, determine the width using the perimeter formula, which reveals the width to be 10 yards. Then calculate the length as six times the width, yielding a length of 60 yards, and finally calculate the area to be 600 square yards.
Step-by-step explanation:
The question asks to find the area of a rectangle where the length is six times its width and the perimeter is 140 yards. Let's denote the width of the rectangle as w and the length as 6w, since the length is six times the width. The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where l is the length and w is the width.
Given that P = 140 yd, we can set up the equation:
2(6w) + 2w = 140
By simplifying, we obtain:
12w + 2w = 14014w = 140
Dividing both sides by 14 yields:
w = 10
Now that we know the width is 10 yards, we can find the length:
l = 6w = 6(10) = 60
The formula for the area (A) of a rectangle is A = lw. Subsequently, we have:
A = 60 yards × 10 yards =
600 square yards
Therefore, the area of the rectangle is 600 square yards.