Algebra question

Question

A wire of length P is cut into two unequal pieces.
The first piece forms a square such that its side is always equal to a natural number.
The second piece forms a rectangle such that its width equals the double of the side of the square and its length equals the treble of the side of the square.

If the perimeter of the square is 20 cm, find in terms of P (where P represents the length of the wire) an expression for the perimeter of the rectangle.






The square has a length of 2 cm, find the dimensions of the rectangle hence calculate the size of the wire used.

Answer 1

There are two pieces of wire.  The length of one is equal to the perimeter of the square, and the length of the second is equal to the perimeter of the rectangle.  Together they are length P.

 

P = perimeter of square + perimeter of rectangle

P = 20 cm + perimeter of rectangle

perimeter of rectangle = P - 20 cm

 

square with length 2 cm has perimeter 4(2 cm) = 8 cm

rectangle width = 2(2 cm) = 4 cm

rectangle length = 3(2 cm) = 6 cm

rectangle perimeter = 2(4 cm) + 2(6 cm) = 20 cm

P = 20 cm + 8 cm = 28 cm