Question 845771: A rectangle and an equilateral triangle have the same perimeter. The length of the rectangle is six times the width. Each side of the triangle is 14 cm. Find the length and width of the rectangle.
(a) If L is the length of the rectangle, then the width of the rectangle is Incorrect: Your answer is incorrect. .
(b) Write an expression for the perimeter of the rectangle.
2L + 2( )L
(c) Simplify the expression you wrote for the perimeter of the rectangle.
****This was part of my online hw but I am not understanding what i am doing.****
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! First let's write down what the formulas for the different perimeters are.
The perimeter of a triangle is
P = a+b+c, where a,b,and c are the lengths of the different legs of the triangle.
Next, let's write down the perimeter of a rectangle.
P = 2L + 2W, where L and W are length and width, respectively.
The problem says that for the rectangle the length L is 6 times greater than the width. Let's translate that into a mathematical statement. Whenever you see "times" that means multiply. Whenever you see "is" that means "=". In other words, for this rectangle, the length L = 6W.
Okay, now let's briefly go back to the triangle problem. The problem tells us that each leg is 14cm. That means it's an equilateral triangle. Now remember what the formula for the perimeter of a triangle says.
P = a+b+c. Therefore the perimeter of the triangle is
P = 14+14+14 since each leg is 14cm. Since all the legs are the same, a short-hand way to write a sum of the same numbers is to multiply one of the leg's length, in this case 14 by the number of legs, in this case 3. So, a simpler way of writing the perimeter is this:
P = 14(3).
Therefore the perimeter is 42cm. Now that we know what the perimeter of the rectangle is we can find out the lengths of the rectangle because the problem tells us that the triangle and the rectangle's perimeter are the same.
So, let's go back to the formula for the perimeter of a rectangle,
P = 2L + 2W
Remember that L =6W. And we know that P = 42, so now we just plug in the values and find the individual values for L and W.
42 = 2(6w) + 2W
Now simplify and combine like terms on the right side.
42 = 12w + 2W
42 = 14w
Divide each side by 14
W = 3cm. Now that we know the width is 3cm we can find out the length since we know that L = 6w. Therefore L = 6(3) = 18cm.
Let's plug in these values to see if the perimeter comes out to 42cm
P = 2(18) + 2(3)
P = 36 + 6
P = 42. It checks out so the the values for the length and width are correct.
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