SOLUTION: The lenght of a five-pound note is 5 mm less than twice the width. The area is 9450 mm sq. Find the dimensions of five-pound note.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The lenght of a five-pound note is 5 mm less than twice the width. The area is 9450 mm sq. Find the dimensions of five-pound note.      Log On


   

Question 548636: The lenght of a five-pound note is 5 mm less than twice the width. The area is 9450 mm sq. Find the dimensions of five-pound note.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a rectangle:
A+=+L%2AW but the length, L, is given as:
L+=+2W-5 "The length...is 5 mm less than twice the width".
and the area, A, is given as A+=+9450 sq.mm., so...
9450+=+%282W-5%29%28w%29 Simplify.
2W%5E2-5W-9450+=+0 Solve this quadratic equation using the quadratic formula: W+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F2a. a = 2, b = -5, and c = -9450
W+=+%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%282%29%28-9450%29%29%29%2F2%282%29 Evaluate this to get:
W+=+70 or W+=+-67.5 Discard the negative solution as width is a positive quantity.
W+=+70mm and...
L+=+2W-5
L+=+140-5
L+=+135mm.