SOLUTION: The length of a rectangle is 5m less than twice the width, and the area of the rectangle is {{{52m^2}}} . Find the dimensions of the rectangle. I need help finding the length an

Algebra ->  Length-and-distance -> SOLUTION: The length of a rectangle is 5m less than twice the width, and the area of the rectangle is {{{52m^2}}} . Find the dimensions of the rectangle. I need help finding the length an      Log On


   

Question 1182008: The length of a rectangle is 5m less than twice the width, and the area of the rectangle is 52m%5E2 . Find the dimensions of the rectangle.
I need help finding the length and width please
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
L and w
system%28L=2w-5%2Cw%282w-5%29=52%29

2w%5E2-5w-52=0

4 & 13 ?
(2w 4)(w 13)
No.
13 & 4 ?
(2w 13)(w 4)
Maybe.

%282w-13%29%28w%2B4%29=0
2w-13=0
w=13%2F2=highlight%286%261%2F2%29----------width
highlight%28L=8%29-----------length

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let w be the width, in meters;

then the length is (2w-5) meters, according to the condition.



Write the area equation

    w*(2w-5) = 52 m^2.



From the equation,

    2w^2 - 5w - 52 = 0.



Use the quadratic formula

    w%5B1%2C2%5D = %285+%2B-+sqrt%285%5E2+-+4%2A2%2A%28-52%29%29%29%2F%282%2A2%29 = %285+%2B-+sqrt%28441%29%29%2F4 = %285+%2B-+21%29%2F4.



You need the positive root  w = %285+%2B+21%29%2F4 = 6.5 m.     



ANSWER.  The width is 6.5 meters;  the length is  2*6.5 - 5 = 8 meters.



CHECK.   6.5*8 = 52 m^2.    ! Correct !


Solved.