Question

Question #c835c

Answer 1

The length is 9, and the width is 12.

Explanation:

To understand the math behind us, let's define this problem using mathematical equations:
Area = length x width, or `A = l*w`
And it is given that the ratio of width to length is 3:4, or `3w = 4l`.
Now I am just going to set our given area, 108, to length x width
`108 = l*w`
We can divide by three for our second equation `3w=4l` to get w on its own: `w=(4/3)l`
Now that we have defined `w` in terms of `l`, we can sub it into our first equation:
`108 = l*(4/3)l`, or `108 = (4/3)l^2`.
To solve for l, we first divide by 4/3 and take the square root, giving
`l = 9`. To solve for w now, we can sub our new `l` value into the original equation `108 = l*w`, giving `108=9w`, and when we divide by 9 on both sides we are left with `w = 12`.