Answer:
The rectangle: <u>L = 40 yards. W = 5 yards</u>
The square: The length and width are both <u>5 yards</u>.
Step-by-step explanation:
<u>Let L and W be the length and width of the rectangle. </u>
<u>Let l and w be the length and width of the square.</u>
Area for each is:
Rectangle: L*W
Square: l*w
We are told that <u>L*W + l*w = 225 yards^2</u>
We are also told that
<u>L = 8W </u>
and that
<u>l = W</u>
Since the sides of a square are all equal, w is also W: <u>w=W</u>
Summarizing and substituting:
L*W + l*w = 225 yards^2
(8W)*W + W*W = 225 yards^2
8W^2 + W^2 = 225 yards^2
9W^2 = 225 yards^2
W^2 = 25
W = 5 feet
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Therefore, since L = 8W <u>,</u> <u>L = 40 yards. W = 5 yards</u> for the rectangle.
The square: l=W, so <u>l = 5 yards, and thus w=5 yards</u>
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Check:
Do a rectangle of 40' x 5' plus a square of 5' x 5' have a total combined area of 225 yards^2?
40yd x 5yd + 5yd x 5yd = 225 yards^2?
200 yd^2 + 25 yd^2 = 225 yards^2?
YES
