Using a quadratic equation to work application problems


Jack has a section of his lawn that is 16 feet wide by 24 feet long. He wants to put in a garden with a walking path along two sides. How wide should the walking path be to make sure that he has 240 square feet of space to grow his plants?

This is a good problem. But to solve using a quadratic equation, the paths need be perpendicular, not parallel. So you set up the problem as (24-x)(16-x) = 240. When you simplify that it comes out to x2 - 40x + 144 = 0. 40 must be the sum of two numbers when multiplied together equal 144. That would be 4 and 36. Therefore the equation would then become (x-4)(x-36) = 0 and the two solutions are x = 4 and x = 36. Only x = 4 makes sense so the paths are 4 feet wide.

One side of a rectangle is 7cm more thatn the other. If the diagonal of the rectangle is 13cm find the dimensions of the rectangle

One side of a rectangle is 7cm more than the other. If the diagonal of the rectangle is 13cm find the dimensions of the rectangle