Oh, dude, the greatest area of a rectangle with a perimeter of 50 would be a square, right? So, if you divide the perimeter by 4, you get the side length of the square, which is 12.5. Then you just square that to get the area, which is 156.25. Easy peasy, lemon squeezy!
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P = 2(L + W)
50 = 2(L + W)
25 = L + W
Let L = x, so W = 25 - x
A = LW
A = x(25 - x)
A = -x2 + 25x
Since the parabola that represents the above equation opens downward, we have a maximum point (the y-coordinate value of the vertex of the parabola, gives us the maximum value of the area).
vertex x-coordinate value = - b/2a = - 25/-2 = 25/2
vertex y-coordinate value = -(25/2)2 + 25(25/2) = - 252/4 + 252/2 = - 252/4 + 2(252)/4 = 252/4 = 156.25
Thu, the maximum area will be 156.25 unit2.
The perimeter of a rectangle of dimensions 50 yards x 100 yards is 300 yards.
The formula to calculate perimeter of a rectangle is P=2L+2W P= 2(15) + 2(10) P= 30 +20 P = 50
From the statement of the problem, if w is the width, the area is 2w2 , the product of the width and the length, which is stated to be twice the width. Since 2w2 must be less than 50, w2 < 25, and the width must be less than 5 meters.
Answer: 30 yards. Explanation: let's say it is L yards long and W yards wide. Then perimeter is 2L+2W The area is LxW=50 So Since LW=50, we substitute L=2W and write 2W(W)=2W^2=50. so W^2=50/2=25 and W=5 Now 2W=10 which is L So is it 10 yards long and 5 yards wide Let's check that. Area is 10x5=50 as desired and Length is 10 which is twice 5 as desired Now perimeter is 2L+2W=2(10)+2(5)=20+10=30 yards.
x=width x+25=length 4x+50=130 4x=80 x=20 width is 20 length is 45