word problem

Question

The length of a rectangular piece of steel in a bridge is 5 meters less than double the width. The perimeter of the piece of steel is 38 meters. Find the length of the piece of steel. Find the width of the piece of steel

Answer 1

First, write an equation that corresponds with the information in the word problem;  L=length, w=width.

 

Perimeter= L+L+W+W, where L= 2W-5.  Because the perimeter is 38 meters, 2L+2W= 38.  Substitute 2W-5 for L and solve:

 

(2W-5) + (2W-5) + W + W=38.  Combine like terms: 4W-10+2W=38 becomes 6W-10=38.  Now add 10 to both sides and you get 6W=48.  Divide both sides by 6, and W=8.  Now we know that the width is 8.  If the length is twice the width minus 5, the length is (2x8)-5 which is 11.  W=8,L=11

Answer 2

Hi Renee,

 

Let the width of the piece of steel be x

 

The length of a rectangular piece of steel in a bridge is 5 meters less than double the width.

 

Length = 2x-5

 

Perimeter of the piece of steel = 38 meters

 

Perimeter of rectangle=2(length+width)

 

38=2(2x-5+x)

 

38=2(3x-5)

38=6x-10

38+10=6x-10+10

48=6x

 

48/6=6x/6

8=x

 

The width of the piece of steel=8 meters

 

The length of the piece of steel=2x-5=2(8)-5=16-5=11meters