SOLUTION: 1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm. Find the width of the rectangle. 2.find the length of the side of a square that is equal in area

Algebra ->  Rectangles -> SOLUTION: 1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm. Find the width of the rectangle. 2.find the length of the side of a square that is equal in area      Log On


   

Question 1209976: 1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm. Find the width of the rectangle.
2.find the length of the side of a square that is equal in area to a rectangle measuring 45cm by 5cm.
I will be glad if you could help solve
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm.
Find the width of the rectangle.
2.find the length of the side of a square that is equal in area to a rectangle measuring 45cm by 5cm.
I will be glad if you could help solve
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

(1)  Let x be the width of the rectangle.

     Write an equation for the area

          9*x = %2824%2F4%29%5E2.


     Simplify and find x

          9x = 6%5E2

          9x = 36

           x = 36/9 = 4.


     ANSWER.  The width of the rectangle is 4 cm.

Solved. 


(2)  Let x be the length of a side of the square.


     Write an equation for the area

         x%5E2 = 45*5.


     Simplify and find x

         x%5E2 = 225

         x = sqrt%28225%29 = 15.


     ANSWER.  The side of the square is 15 cm.

Solved.



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
1.A rectangle 9cm long is equal in area to a spuare which has a perimeter of 24cm. Find the width of the rectangle.
2.find the length of the side of a square that is equal in area to a rectangle measuring 45cm by 5cm.
 I will be glad if you could help solve

1.  With perimeter of square being 24 cm, length of 1 side of square = 24%2F4 = 6 cm
    As such, area of square = 6 * 6  = 62 = 36 sq cm 

    Let width of rectangle be W
    With length of rectangle being 9 cm, and its area being the same as square's
    area (36 sq cm), we get:  LW = 62
                              9W = 36
    Width of rectangle, or W = 36%2F9 = 4 cm

2. Rectangle’s dimensions: 45 cm by 5 cm, so area = 45(5) = 225 sq cm
    With length of 1 side of square being S, area of square = S2 
    Since areas of square and rectangle are the same, S2 = 225
    Length of 1 side of the square, or S = sqrt%28225%29 = 15 cm