A doormat has an area of 912 square inches. Its perimeter is 124 inches. What are the dimensions of the doormat?
Let x = width
Let y = length
Area of rectangle is length x width, so
A = xy
912 = xy
Perimeter of rectangle is 2*(length + width), so
P = 2(x + y)
124 = 2(x + y)
62 = x + y
Now that you have two equations tow unknowns, we can solve for x and y. From the second equation, we can write an expression for y and substitute it to the first equation:
62 = x + y
y = 62 - x
912 = xy
912 = x(62 - x)
912 = 62x - x^2
Now continue solving this. Hope this helps~ `u`
width ---- x
length ----y
2x + 2y = 124
x+y=62
y = 62-x
xy = 912
x(62-x) = 912
62x - x^2 - 912 = 0
x^2 - 62x + 912 = 0
(x-24)(x-38) = 0
x = 24 or x = 38, then
y = 38 or y = 24
the doormat is 24 by 38
The perimeter of a doormat is 124 inches. It is 22 inches wide. How long is it
To find the dimensions of the doormat, we need to solve a system of equations using the given information.
Let's assume the length of the doormat is L inches, and the width is W inches.
According to the problem, the area of the doormat is 912 square inches, which can be expressed as:
L * W = 912 ...(1)
Also, the perimeter of the doormat is 124 inches, which can be expressed as:
2L + 2W = 124 ...(2)
To solve this system of equations, we can use the method of substitution or elimination. In this case, let's use the substitution method.
Solve equation (2) for W:
2L + 2W = 124
2W = 124 - 2L
W = (124 - 2L)/2
W = 62 - L ...(3)
Now substitute equation (3) into equation (1):
L * (62 - L) = 912
62L - L^2 = 912
L^2 - 62L + 912 = 0
This is a quadratic equation. We can solve it using factoring, completing the square, or the quadratic formula. Let's use factoring in this case.
(L - 38)(L - 24) = 0
Setting each factor equal to zero, we get:
L - 38 = 0 or L - 24 = 0
Solving these equations, we find:
L = 38 or L = 24
If L = 38, substitute it back into equation (3) to find W:
W = 62 - L
W = 62 - 38
W = 24
So, one possible solution is L = 38 inches and W = 24 inches.
If L = 24, substitute it back into equation (3) to find W:
W = 62 - L
W = 62 - 24
W = 38
So, another possible solution is L = 24 inches and W = 38 inches.
Therefore, the dimensions of the doormat can be either 38 inches by 24 inches or 24 inches by 38 inches.