Answer: The width is: " 10 m " .
_____________
To express this answer as an "exponential expression" ; we can write this answer as: " 10¹ m " .
_____________
Also, we can write the width as an unsimplified "exponential expression" as:
" [tex]\frac{10^4}{10^3}[/tex] m " .
_____________
Step-by-step explanation:
Area, "A" = L (length) * w (width ;
_____________
Since: " A = L * w " ;
and since we are to find the width; "w" ;
let us rewrite the equation;
to isolate "w" on one side of the equation:
_____________
" A = L * w " ;
Divide Each Side of the equation by "L" ;
A / L = (L * w) / L ;
The " L's " on the "right-hand side" of the equation "cancel out" ;
{since: " L / L = 1 " } ;
and we have:
A / L = w ;
↔ w = A / L ;
_____________
Now, we are given: "A = 10⁴ m² " ;
" L = 10³ m " [the 'length' (from image attached) ] ;
We can substitute these values in our equation:
_____________
w = A / L ;
" [tex]w = A/L = \frac{10^4 m^2}{10^3 m} = 10^{(4-3)} m^{(2-1)} = 10^1m^1 = 10 m[/tex] ."
The width, "w" = 10 m .
_____________
Let us check our answer:
Area (A) = L (length) * w (width) ;
→ 10⁴ m² ≟ 10³ m * 10 m ? ;
_____________
→ 10⁴ m² ≟ 10³ * 10¹ m * m ? ;
_____________
→ 10⁴ m² ≟ 10⁽³⁺ ¹⁾ * m * m ? ;
→ 10⁴ m² ≟ 10⁴ m² ? Yes!
_____________
Other: Let us further check our answer; in a different format:
_____________
Area (A) = L (length) * w (width) ;
→ 10⁴ m² ≟ 10³ m * 10 m ? ;
_____________
→ 10,000 m² ≟ 1,000 m * 10 m ?
→ 10,000 m² ≟ 10,000 m * m ≟ 10,000 m² ? Yes!
_____________
Hope this is helpful.
Best of luck in your academic endeavors—& within "Brainly" !
_____________
