SOLUTION: Please help me to solve this word problem: A square and a rectangular plot of land have same perimeter. If the square is of side 40 m and rectangle is of length 5 dam, then what

Question 518997: Please help me to solve this word problem:
A square and a rectangular plot of land have same perimeter. If the square is of side 40 m and rectangle is of length 5 dam, then what is the area of the rectangle?
This the exact question copied from the Maths Olympiad practice book. Also please tell me the method.
Thank you
Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
To find the area of the rectangle, you need to find the length and the width of the rectangle.
To solve this problem you need to start by writing an equation using what you know.
First, you know the perimeters of the square plot and rectangular plot are equal.
square perimeter = 4s (where s is the length of each side)
rectangular perimeter = 2L + 2W (where L is length and W is the width of the rect)
so 4s = 2L + 2W
Next, you know that the square has a side length of 40m. So plug that into the equation above for s:
4s = 2L + 2W
4(40) = 2L + 2W
160 = 2L + 2W
Finally, you know that the length of the rectangle is 5m (I am assuming you meant to write m). So plug that into the equation for L:
160 = 2L + 2W
160 = 2(5) + 2W
160 = 10 + 2W
Now solve for the width.
160 = 10 + 2W
150 = 2W
75 = W
So the width of the rectangle is 75m.
Now to find the area of the rectangle, use the area formula:
A = LW (A=area, L=length, W=width)
A = LW
A = (75)(5)
A = 375
So the area of the rectangle is 375 meters squared.
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