Question

A rectangle with an area of 24 square units has length x+1 and width 4x-6. find the value of x.

Answer 1

`area = length \cdot width \\ \\A = 24 s^2 \\ \\ l=x+1 , \ \ w=4x-6 \\ \\ A=lw\\ \\24 =(x+1)(4x-6)`


`24 =4x^2-6x+4x-6 \\ \\4x^2-6x+4x-6 -24=0\\ \\4x^2-2x-30=0 \ \ / :2\\ \\2x^2-x-15=0 \\ \\a=2, \ b=-1 , c= -15`


`\Delta =b^2-4ac = (-1)^2 -4\cdot2\cdot (-15) = 1+120=121\\ \\x_(1)=(-b-√(\Delta) )/(2a)=(1-√(121))/(2*2 )=( 1-11)/(4)=(-10)/(4)=- (5)/(2) \\ \\x_(2)=(-b+√(\Delta) )/(2a)=(1+√(121))/(2*2 )=( 1+11)/(4)=(12)/(4)=3 \\ \\Use \ positive \ value \ of \ x : \\ \\ x =3`