Question 623639: What are the dimensions of a rectangle that has a perimeter of 38 units an an area of 60 square units? Found 2 solutions by ankor@dixie-net.com, math-vortex:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! what are the dimension of a rectangle that has a perimeter of 38 units an an area of 60 square units.
:
Perimeter equation
2L + 2W = 38
simplify divide by 2
L + W = 19
W = (19-L)
:
The area equation
L * W = 60
Replace W with (19-L)
L(19-L) = 60
19L - L^2 = 60
0 = L^2 - 19L + 60
Factors to
(L-4)(L-15) = 0
Two solutions, but assume L is the larger value
L = 15 units
Find W
W = 19 - 15
W = 4 units
:
Check the perimeter and the area with these values
Hi, there--
The Problem:
What are the dimensions of a rectangle that has a perimeter of 38 units an an area of 60 square units?
A Solution:
Let W be the width of the rectangle.
Let L be its length.
Now we need to write two equations that use information in the problem about the length and width
of the rectangle.
{1} The rectangle has a perimeter of 38 units.
Perimeter means the distance around the outside of the rectangle. We calculate the perimeter P by
adding the two widths and two lengths. In an equation, we write this relationship as
2W + 2L = 38
{2} The area of the rectangle is 60 square units.
The formula for the area of a rectangle is length times width. We can express with relationship
by the equation,
L * W = 60
Now we have a system of two equations with two variables. We will use the substitution method
to find the length and width.
Divide every term in the first equation by 2.
2W + 2L = 38
W + L = 19
Rewrite this equation in "W=..." form. (Subtract L from both sides.)
W = 19 - L
We see that W and 19-L are equivalent. Make this substitution in the second equation.
L * W = 60
L * (L - 19) = 60
Multiply to clear the parentheses.
L^2 - 19L = 60
Subtract 60 from both sides of the equation.
L^2 - 19L - 60 = 0
We will solve this equation by translating the it to factored form. We need two numbers whose
product is 60 and whose sum is -19. The numbers are -15 and -4. The equation in factored form is
(L - 15)(L - 4) = 0
The solutions to this equation are
L - 15 = 0 OR L - 4 = 0
L = 15 OR L = 4
If L=15, then the W is 4 units since the area is 60 square units and 15*4=60.
By similar reasoning, if L=4, then the width is 15 units.
We need to check that these values for length and with give the correct perimeter.
15 + 15 + 4 + 4 = 38, so all is well. THe dimensions of the rectangle are 4 units and 15 units.
Feel free to email me if you have questions about the solution.
Ms.Figgy
math.in.the.vortex@gmail.com
