math word problem

Question

define variables, write an equation, and then use the equation in the solving process.
 
The length of a rectangular frame is 3 cm more than the width. The area inside the frame is 70 square cm. Find the width of the frame.

Answer 1

Let L = length of the frame. Let W = the width of the frame

L=3+W

Area = A = 70 = LW = (3+W)W = 3W + W²

W² + 3W - 70 = 0

You could use the quadratic formula or complete the square, but this quadratic equation is easily factored

(W+10)(W-7) = 0

Then set each factor = 0

W-7=0 W=7 L=3+W=3+7=10

Width = 7cm Length = 10 cm

W+10=0 or W=-10, but this solution can be ignored as negative lengths don't make sense

If somehow a negative length had some possible meaning, you'd get W=-10 cm and L=-7 cm

-7 is 3 more than -10, and -10 times -7 = 70 square centimeters.