SOLUTION: Ok, there is a problem in my worksheet that gives me the following information:
Perimeter of the Rectangle: 68cm
Area of the Rectangle: 144sq. cm
and its asking for the length
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Question 279050: Ok, there is a problem in my worksheet that gives me the following information:
Perimeter of the Rectangle: 68cm
Area of the Rectangle: 144sq. cm
and its asking for the length of the diagonal, how do i solve this? it does not give any dimensions (Width, Height)
If you can help me, id love it. Thank You
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
2L + 2W = 68 ___ L + W = 34
L * W = 144
by Pythagoras, D^2 = L^2 + W^2 = (L + W)^2 - 2 LW
D^2 = 34^2 - 2(144)
D = sqrt(868)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
gives me the following information:
:
Start by using L for Length, W for width
:
Perimeter of the Rectangle: 68cm
2L + 2W = 68
Simplify, divide by 2
L + W = 34
or
W = (34-L)
:
Area of the Rectangle: 144sq. cm
L * W = 144
Substitute (34-L) for W
L * (34-L) = 144
34L - L^2 = 144
Arrange as a quadratic equation
-L^2 + 34L - 144 = 0
We have to solve this using the quadratic formula
In this equation: x=L; a=-1; b=34; c=-144
:
:
Two solutions
L =
L = +4.958
and
L =
L = +29.0415
:
the larger 29.0415 cm is the length
the smaller 4.958 cm is the width
:
Check our solution by finding the perimeter with a calc
2(29.0415) + 2(4.958) = 67.999 ~ 68
:
and its asking for the length of the diagonal, now we have the dimensions:
Use pythag for this: c = ,
:
c =
c = 29.462 is the diagonal
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