Question 86695
Question:


Solve algebraically using only one variable. The length of a rectangle is two more than twice its width. If the area of the rectangle is 84, find the length and width.


Answer:


Assume that width of the rectangle = x units.(since here length is given in terms of width...so first assume width = x units)


Then twice the width = 2*x = 2x

Two more than twice the width = 2x + 2



Then length of the rectangle  = 2x + x units



Now area of the triangle is given as = 84


By the formula, area = length * width



==> length * width = 84



==> (2x + 2 ) * x = 84



Remove the parenthesis....



==> 2x * x + 2 * x = 84



==> {{{ x^2 + x - 42 = 0 }}}




This is  a quadratic equation....you can solve it by either factorisation method or using quadratic formula...



Factorisation method....


{{{ x^2 + x - 42 = 0 }}}


Here you have to find out two numbers whose sum is 1 and their product is -42



Such two numbers are 7 and -6



Now split the middle terms using this numbers.....



{{{ x^2 + 7x - 6x  - 42 = 0 }}}



Now group the terms....


{{{ (x^2 + 7x) - (6x  + 42) = 0 }}}




Now take out the common term from each group.....




{{{ x(x + 7) - 6(x  + 7) = 0 }}}



Here (x+ 7 ) is common ib both the groups...so again take it outside...




==> (x + 7)( x- 7) = 0



==> either x + 7 = 0 or x - 6 = 0




==> x = -7 or   x = 6



So the solution of the given expression is   x = -7 or   x = 6



You can check the answers using quadratic formula, {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}



Then you will get the same answers....




Hope you found the explanation useful...



Warm Regards.



Praseena.