To find the length of a rectangular painting given its area and width, we can use the formula for the area of a rectangle:
[tex]\[ \text{Area} = \text{Width} \times \text{Length} \][/tex]
where:
- Area = 8256 cm² (provided in the question)
- Width = 86 cm (provided in the question)
- Length = ? (this is what we need to find)
We need to solve for the Length. Rearranging the formula to solve for Length, we get:
[tex]\[ \text{Length} = \frac{\text{Area}}{\text{Width}} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ \text{Length} = \frac{8256 \, \text{cm}^2}{86 \, \text{cm}} \][/tex]
Perform the division:
[tex]\[ \text{Length} = \frac{8256}{86} \][/tex]
Calculate the result:
[tex]\[ \text{Length} = 96 \, \text{cm} \][/tex]
So, the length of the painting is:
[tex]\[ \boxed{96 \text{ cm}} \][/tex]
