if a rug's perimeter is 17cm and the area is 13cm, what are the reasurments for the length and width?
Are you sure you copied this problem correctly?
A rug with a perimeter of 17 cm wouldn't be large enough to hold my big toe.
this is copied correctly. the teacher wanted to keep it simple
Your teacher should have stated that the area is 13 cm^2.
If your teacher tried to make it simple, then he/she did not do such a good job.
I did it by algebra and it led to a quadratic equation.
length - x
width - y
2x + 2y = 17
x + y = 8.5
also xy = 13, so y = 13/x
x + 13/x = 8.5
x^2 - 8.5x + 13 = 0
2x^2 - 17x + 26 = 0
(x-2)(2x - 13) = 0
x = 2 or x = 6.5
if x = 2 , then y = 6.5
if x = 6.5, then y = 2
so the "rug" is 2 cm by 6.5 cm, and as Ms Sue noted, probably just big enough to fit into a doll house.
I have a 4th grade "guess" at that answer is rather stretching it.
That is not 4th grade homework
To find the measurements for the length and width of the rug, you can use a system of equations. Let's assign variables: let L represent the length of the rug and W represent the width.
1. Perimeter equation: The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the length and width are each counted twice (since there are two sides of each). So, the perimeter equation becomes:
2L + 2W = 17cm
2. Area equation: The area of a rectangle is calculated by multiplying the length and width. Therefore, the area equation is:
L * W = 13cm²
To solve this system of equations, we can use substitution or elimination method. Let's use substitution:
1. Rearrange the perimeter equation to solve for one variable. Solve it for L:
2L = 17cm - 2W
L = (17cm - 2W) / 2
2. Substitute the value of L in the area equation:
L * W = 13cm²
[(17cm - 2W) / 2] * W = 13cm²
3. Simplify the equation and solve for W:
(17cm - 2W) * W = 26cm²
17W - 2W² = 26cm²
Rearrange the equation:
2W² - 17W + 26cm² = 0
4. Solve for W using factoring, quadratic formula, or completing the square. In this case, we can factor:
(2W - 13) (W - 2) = 0
This gives two possible values for W:
W = 13/2cm or W = 2cm
5. Plug the values of W back into the length equation and solve for L:
Using W = 13/2cm:
L = (17cm - 2(13/2cm)) / 2
L = 4cm
Using W = 2cm:
L = (17cm - 2(2cm)) / 2
L = 6.5cm
Therefore, the possible measurements for length and width are:
L = 4cm, W = 13/2cm or L = 6.5cm, W = 2cm