Is there an easier way to solve the following problem without going through 100 guesses trying to find two numbers that total de area and the perimeter. ps I'm the mom trying to explain to my kid
The perimeter of a rectangular banner is 72 inches. The width of the banner is 1/3 it's length what is the area of the banner ? 27 and 9. Area is 243
Thanks for your help
P = 2L + 2W
72 = 2L + 2(1/3)L
72 = 2 2/3L
72 = (8/3)L
72/(8/3) = L
72 * (3/8) = L
216/8 = L
27 = L
Thanks. The teacher has not taught division that is the problem. I don't get how else they can get the answer without dividing is there another way. This is crazy
I don't know. I suggest you make an appointment and talk with the teacher. The teacher may have another method.
Yes, there is an easier way to solve this problem without going through 100 guesses. Let me explain the process step by step.
Step 1: Understand the problem
We are given that the perimeter of a rectangular banner is 72 inches, and the width is 1/3 of its length. We need to find the area of this banner.
Step 2: Set up the equations
Let's use "L" to represent the length of the banner, and "W" to represent the width.
From the problem statement, we know that:
Perimeter = 2 * (Length + Width) = 72 inches
Width = (1/3) * Length
Step 3: Solve the equations
Now we can substitute the value of width in terms of length into the perimeter equation. Let's do that:
2 * (Length + (1/3) * Length) = 72
Simplify the equation:
2 * (4/3) * Length = 72
Multiply both sides by 3/2 to isolate the Length:
Length = (72 * 3/2) / (2 * 4)
Length = (216/2) / 8
Length = 108 / 8
Length = 13.5 inches
Step 4: Calculate the width
We can now find the width by substituting the length value we found into the width equation:
Width = (1/3) * 13.5
Width = 4.5 inches
Step 5: Calculate the area
Finally, we can calculate the area of the rectangular banner using the formula:
Area = Length * Width
Area = 13.5 * 4.5
Area = 60.75 square inches
Therefore, the area of the banner is 60.75 square inches.
By following these steps, you can solve the problem without having to make 100 guesses.