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 20 meters. Find the length of the piece of steel. Find the width of the piece of steel.

A) Width: 5 meters, Length: 10 meters
B) Width: 7.5 meters, Length: 15 meters
C) Width: 6 meters, Length: 12 meters
D) Width: 4 meters, Length: 8 meters
E) None of the above.

Answer 1

Using the relationship between the length and width of the piece of steel given in the problem, along with the perimeter formula for rectangles, we can solve for the width and length. The width is found to be 5 meters and the length 10 meters, which corresponds to option A.

Step-by-step explanation:

To find the length and width of the piece of steel, we set up the following equivalent expressions based on the information provided:

• The length (L) is 5 meters less than double the width (W), so L = 2W - 5.
• The perimeter (P) is 20 meters, and for a rectangle, P = 2L + 2W, so substituting in the expression for L gives P = 2(2W - 5) + 2W.

Let's calculate:

• 20 = 4W - 10 + 2W
• 20 = 6W - 10
• 30 = 6W
• W = 5 meters
• L = 2(5) - 5 = 10 - 5 = 10 meters

Therefore, the width of the piece of steel is 5 meters, and the length is 10 meters.

Comparing these findings against the provided options, we select option A) Width: 5 meters, Length: 10 meters as the correct answer.