Question

The figure in the attachment. AB= 14 cm, BC=11 cm and AK=BL=CM=DN=xcm. If the area of KLMN is now 97 cm square, find x.
http://imageshack.us/photo/my-images/831/quadratic.jpg/

Answer 1

You could start by setting up the equations that describe the figure. Sometimes that helps you see a path toward a solution.

Area of ABCD = (11)(14)

AB = AK + KB = x + KB
AD = AN + ND = x + AN
CD = CM + MD = x + MD
BC = BL + LC = x + LC

Now you have the side lengths of the rectangle KLMN. With the side lengths, you can set up the area equation, and you know that area of KLMN is 97.

You might have to do a little more work, but maybe this will get you started.

Answer 2

The question in the book is to form a quadratic equation inorder to solve it

Answer 3

right, I guess I jumped ahead too far when I said you had the side lengths of KLMN.

You do have the side lengths of the short and long parts of the outside rectangle edges... that's what I wrote in the previous post. Now you need to use these side parts and the fact that they form right triangles with the inside diagonal lines that are KLMN... that would allow you to write two equations of the side lengths of KLMN that would be in terms of x and 11 and 14 (from the outside rectangle).

Then, Area of KLMN = 97 = (side length equation for KL) * (side length equation for LM)

It will definitely be quadratic once you start multiplying those x-term equations by each other.