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

Algebra ->  Pythagorean-theorem -> 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      Log On


   

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) About Me  (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) About Me  (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
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: x=L; a=-1; b=34; c=-144
L+=+%28-34+%2B-+sqrt%2834%5E2-4%2A-1%2A-144+%29%29%2F%282%2A-1%29+
:
L+=+%28-34+%2B-+sqrt%281156-576+%29%29%2F%28-2%29+
:
L+=+%28-34+%2B-+sqrt%28580+%29%29%2F%28-2%29+
Two solutions
L+=+%28-34+%2B+24.083%29%2F%28-2%29+
L = %28-9.917%29%2F%28-2%29
L = +4.958
and
L+=+%28-34+-+24.083%29%2F%28-2%29+
L = %28-58.083%29%2F%28-2%29
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 = sqrt%28a%5E2+%2B+b%5E2%29,
:
c = sqrt%2829.0415%5E2+%2B+4.958%5E2%29
c = 29.462 is the diagonal