an art class is planning to paint a rectangular mural with an area of 60 square feet .It has to be at least 4 feet high but no more than 6 feet high. How long could it be if the length and width have to be a whole number
It must be 2 feet wide. 60/2 = 30 feet long.
The factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60
So, which ones meet the requirements? Having the height, you can then figure the length.
mss sue can you show me how to figure this
huh? The height must be 4 or 5 or 6.
Those are the only factors of 60 that are
(a) at least 4
(b) no more than 6
If the height is 4, the length is 60/4 = 15
and similarly for 5 or 6.
To find the length of the rectangular mural, we can use the formula for the area of a rectangle: Area = Length × Width.
Given that the area of the mural is 60 square feet, we need to find two whole numbers (length and width) that when multiplied together equal 60.
Let's start by listing all the possible pairs of factors of 60:
1 × 60 = 60
2 × 30 = 60
3 × 20 = 60
4 × 15 = 60
5 × 12 = 60
6 × 10 = 60
Now, we need to check that each pair satisfies the height requirement of being at least 4 feet but no more than 6 feet.
For the pair 1 × 60, the length is 60 feet, which is more than the maximum allowable height of 6 feet, so this pair is not valid.
For the pair 2 × 30, the length is 30 feet, which is also greater than 6 feet, so it is not valid.
For the pair 3 × 20, the length is 20 feet, which is within the acceptable range.
For the pair 4 × 15, the length is 15 feet, which is less than 4 feet, so it is not valid.
For the pair 5 × 12, the length is 12 feet, which is within the acceptable range.
For the pair 6 × 10, the length is 10 feet, which is within the acceptable range.
Therefore, the valid pairs are 3 × 20, 5 × 12, and 6 × 10.
The length can be either 20 feet, 12 feet, or 10 feet.