Lila is planning to build a rectangular garden in her backyard. She wants the length to be twice the width plus 5 metersIf the area of her garden is 250 square metersthen what is the width? point)
Let the width of the garden be 'w' meters.
So, the length of the garden would be 2w + 5 meters.
We know that the area of a rectangle is given by length times width, so:
Area = Length x Width
250 = (2w + 5) x w
250 = 2w^2 + 5w
Now we have a quadratic equation. Rearranging and setting it equal to zero:
2w^2 + 5w - 250 = 0
We can factorize the equation or use the quadratic formula to solve for 'w'. Factoring, we get:
(2w - 25)(w + 10) = 0
Setting each factor to zero, we get:
2w - 25 = 0 or w + 10 = 0
w = 25/2 or w = -10
w = 12.5 meters (width can't be negative)
Therefore, the width of the garden is 12.5 meters.