SOLUTION: Find the length of a side of a square whose area is the same as that of a rectangle 24 cm. by 30 cm.

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Question 78327This question is from textbook Algebra Structure and Method Book 1
: Find the length of a side of a square whose area is the same as that of a rectangle 24 cm. by 30 cm. This question is from textbook Algebra Structure and Method Book 1

Found 2 solutions by jim_thompson5910, rmromero:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since the areas are equal we can find the area of the rectangle to find the area of the square:

Area of rectangle=base*height=24*30=720
So the area of the rectangle is 720 square centimeters. Now we know the area of the square is 720 square centimeters also. Now we have this relationship:
Area of square=side*side=(side)^2

Let s=side
So we have
Area of square
A=s%5E2
720=s%5E2 Plug in A=720 and solve for s
sqrt%28720%29=sqrt%28s%5E2%29 take the square root of both sides
s=sqrt%28720%29
Now reduce:
s=sqrt%28144%2A5%29
s=sqrt%28144%29%2Asqrt%285%29
s=12%2Asqrt%285%29
So the side of the square is about 26.83 cm long

Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!


Find the length of a side of a square whose area is the same as that of a rectangle 24 cm. by 30 cm.





Find the area of the rectangle first



   Area of Rectangle = Length * width

                     = 24 * 30

                     = 720 sq cm





   Area of rectangle = Area of square

         720sq cm    = 720 sq cm





   Area of the square = s^2

            720 sq cm = s^2

        +sqrt+%28720%29 = s

                26.83  = s