Answer:
[tex]5[/tex]
Step-by-step explanation:
GIVEN: The area of a Little Italy gallery is [tex]588\text{ m}^2[/tex] and has a rectangular shape. If one side of the gallery measures [tex]2x + 4[/tex] and another side measures [tex]8x + 2[/tex].
TO FIND: what is the value of [tex]x[/tex].
SOLUTION:
Length of first side [tex]=(2x+4)[/tex]
Length of second side [tex]=(8x+2)[/tex]
Area of rectangle [tex]=\text{length}\times\text{breadth}[/tex]
[tex]=(2x+4)(8x+2)=16x^2+36x+8=588[/tex]
[tex]\implies[/tex] [tex]16x^2+36x-580=0[/tex]
Solving we get
[tex]x=5,\frac{-29}{4}[/tex]
As [tex]x<0[/tex], the value of [tex]x[/tex] is [tex]5[/tex]
