Question

the rectangle below has an area of $12y^5$ square meters and a width of $3y^3$ meters.
what is the length of the rectangle?
length = $square$ meters

Explanation:

Step1: Recall area formula for rectangle

The area of a rectangle is $A = l \times w$, where $l$ = length, $w$ = width. Rearranged to solve for length: $l = \frac{A}{w}$

Step2: Substitute given values

Substitute $A = 12y^5$ and $w = 3y^3$ into the formula.
$l = \frac{12y^5}{3y^3}$

Step3: Simplify the coefficient

Divide the numerical coefficients: $\frac{12}{3} = 4$

Step4: Simplify the variable terms

Use exponent rule $\frac{y^a}{y^b} = y^{a-b}$: $\frac{y^5}{y^3} = y^{5-3} = y^2$

Step5: Combine results

Multiply the simplified coefficient and variable term.
$l = 4y^2$

Answer:

$4y^2$