Respuesta :
Answer:
The value of [tex]x = \frac{1}{6}[/tex]
The length of the rectangle [tex]= \frac{3}{2}[/tex] cm
The width of the rectangle = [tex]\frac{16}{3}[/tex] cm
Step-by-step explanation:
Step(i):-
Given that area of the rectangle = 8 cm²
Length of the rectangle (l) = 3x+1
width of the rectangle (w) = 2x+5
The area of the rectangle = length × width
Given that area of the rectangle = 8 cm²
Step(ii):-
Now
(3x+1) ( 2x+5) = 8
⇒ 3x(2x+5) +1(2x+5) =8
6 x² + 15x + 2x +5 =8
⇒ 6 x² + 17x -3 =0
⇒ 6 x² + 18x -x -3 =0
⇒ 6 x ( x+3) -1(x+3) =0
⇒ 6x -1 =0 and x +3 =0
[tex]6x = 1[/tex] and x =-3
[tex]x = \frac{1}{6}[/tex]
The length of the rectangle
[tex]= 3 (\frac{1}{6} ) +1 \\= \frac{3}{2}[/tex]
The width of the rectangle
[tex]= 2 (\frac{1}{6} ) +5[/tex]
= [tex]\frac{16}{3}[/tex]
