Problema Solution
The length of a picture frame is one inch less than three times its width. The area of the picture frame is 70 square inches. Find the dimensions of the frame.
Answer provided by our tutors
An equation in the form ax^2+bx+c=0 can be rewritten and solved using:
x = [-b +- root(b^2-4ac)] / 2a
so first we take our formula for area:
l x w = A
and sub in what we know:
(3w - 1)w = 70
Works out to 3w^2 - 1w = 70
Now that can be arranged as:
3w^2 + (-1w) + (-70) = 0
Now feed these numbers into the formula I showed you earlier:
w = [-(-1) +- root((-1)^2 - 4(3)(-70))] / 2(3)
Simplifies to:
w = [1 +- 29] / 6
Since our width can't be negative,
w = [1 + 29] / 6
w = 5
So now we can solve for L:
l x w = A
l x 5 = 70
l = 70/5
l = 14
Check: 5 x 14 = 70