the perimeter of a rectangle is 160m and its area is 1200m^2 find its dimensions
I'll get you started.
√ 1200 = 34.64
then what i seriously have no clue what im doing
With a little trial and error, I found that the dimensions must be 20 by 60
2w + 2l = 160
w+l = 80
l= 80-w
wl = 1200
w(80-w) = 1200
80w - w^2 - 1200=0
w^2 - 80w + 1200 = 0
(w-20)(w - 60) = 0
w = 20 or w = 60
if w = 20, then l = 80-20 = 60
and if w - 60 , then l = 80-60 = 20
So the rectangle is 20 by 60 as Ms Sue found by trial-and-error
To find the dimensions of the rectangle, we can use the formulas for perimeter and area.
Let's assume that the length of the rectangle is represented by 'L' and the width is represented by 'W'.
Perimeter of the rectangle = 2(L + W) = 160
Area of the rectangle = L * W = 1200
From the first equation, we can solve for 'L + W':
2(L + W) = 160
L + W = 160/2
L + W = 80
Now, we have a system of two equations:
L + W = 80
L * W = 1200
To solve this system, we can use substitution or elimination method. Let's solve it using the substitution method.
Rearrange the first equation to find L in terms of W:
L = 80 - W
Substitute this value of L into the second equation:
(80 - W) * W = 1200
Distribute and rearrange the equation:
80W - W^2 = 1200
Rearrange the equation in standard quadratic form:
W^2 - 80W + 1200 = 0
Now we can solve this quadratic equation to find the possible values of W. Using the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / 2a
In this equation:
a = 1 (coefficient of W^2)
b = -80 (coefficient of W)
c = 1200
Using the quadratic formula, we get:
W = (-(-80) ± √((-80)^2 - 4(1)(1200))) / 2(1)
Simplifying:
W = (80 ± √(6400 - 4800)) / 2
W = (80 ± √1600) / 2
W = (80 ± 40) / 2
Simplifying further:
W = (80 + 40) / 2 = 120 / 2 = 60
W = (80 - 40) / 2 = 40 / 2 = 20
So, the possible values of W are 60 and 20.
Now, substitute these values of W back into the first equation to find L:
For W = 60:
L + 60 = 80
L = 80 - 60
L = 20
For W = 20:
L + 20 = 80
L = 80 - 20
L = 60
Therefore, the dimensions of the rectangle can be either 20m by 60m or 60m by 20m.