Quadratic equations

Question

The dimensions of a rectangular garder were 5m by 8m. Each dimension was increased by the same amount. The garden then had an area of 108 m^2. Find the dimensions of the new garden

Answer 1

x + 5 and x + 8 will be the new dimensions of the garden. So (x + 5)(x + 8) = 108. Multiplying the binomials gets us x² + 13x + 40 = 108. Now we have a quadratic so we want it to equal 0. After we subtract 108 from both sides, we get x² + 13x - 68 = 0. This factors to (x + 17)(x - 4)= 0. After setting the factors equal to 0, we get x = -17 and 4. We can't have a negative value so x = 4. This makes the original dimensions 9m x12m.