Question

A rectangle has an area of 24 with a width of 2 3/4 what is the length?

Answer 1

`8(8)/(11)`

Skills needed: 2-d Geometry

Explanation:

1) The area formula for a rectangle is:

`A = l*w`

`A=area`

`l=length`

`w=width`

---> In the problem above, we are given the width and the area and have to solve for the length. We can just plug in the other two values in order to get the third value.

2) Plugging it in:

`24 = l*2(3)/(4)`

In order to solve for L, we need to isolate it. This means we need to get
`l` by itself on one side, and have all other values on the other.

Time to divide by
`2(3)/(4)` on both sides.

`24 / 2(3)/(4) = l * 2(3)/(4) / 2(3)/(4)`

On the right side: The multiplication and division cancel out since it is the same value. We are left with just
`l` (length)

Left side:
`24 / 2(3)/(4) = (96)/(4) / (11)/(4) = (96)/(4) * (4)/(11) = (96)/(11) = 8(8)/(11)`

We just do some fraction division (converting 24 into an improper fraction and the mixed number into an improper fraction --- then flipping the 2nd fraction to now multiply, and getting an improper fraction -- then converting that improper fraction into a mixed number)

In the end, we end up with:
`8(8)/(11)=l`, which means
`8(8)/(11)` is the answer.