Answer: The dimension are 70 by 29
Step-by-step explanation:
[tex]\\[/tex]The are of a rectangle is given as L X B , that means from the first statement , L X B = 2030
[tex]\\[/tex]Also, the Perimeter of a rectangle is given by 2 ( L + B ), that means from the second statement 2 ( L + B ) = 198 , dividing this through by 2 , we have
[tex]\\[/tex]L + B = 99
[tex]\\[/tex]Combing the two equations, we have
[tex]\\[/tex]LB = 2030 ........... 1
[tex]\\[/tex]L + B = 99 ............ 2
[tex]\\[/tex]Solving the resulting simultaneous equation
[tex]\\[/tex]from equation 1 make L the subject , we have
[tex]\\[/tex]L = 2030/B
[tex]\\[/tex]Also, from equation 2 , make L the subject of the formula , we have
[tex]\\[/tex]= 99 - B ............ **
[tex]\\[/tex]Equate the two values of L , we have
[tex]\\[/tex]2030 / B= 99 - B , by cross multiplying , we have
[tex]\\[/tex]2030 = 99B - [tex]B^{2}[/tex]
[tex]\\[/tex]This is the same as [tex]B^{2}[/tex] - 99B + 2030 = 0
[tex]\\[/tex]This is a quadratic equation, solving by quadratic formula
[tex]\\[/tex] L = 70 or 29
[tex]\\[/tex]substituting this value into **
[tex]\\[/tex]B = 29 or 70
[tex]\\[/tex]Therefore the dimensions are 70 X29
