Answer:
50/65
Step-by-step explanation:
we mark the width as w and the length as l
we know that:
[tex]l = w + 15[/tex]
we also know the area of a rectangle is given by:
[tex]area = l \times w[/tex]
since the area is given, we substitute l and get:
[tex]1750 = (w + 15) \times w[/tex]
from this we derive the following quadratic equation:
[tex]{w}^{2} + 15w - 1750 = 0[/tex]
we aolve for w, using the quadratic formula:
[tex]w 1 = \frac{ - 15 + \sqrt{ {15}^{2} - 4 \times 1 \times ( - 1750)} }{2} \\ w 2 = \frac{ - 15 - \sqrt{ {15}^{2} - 4 \times 1 \times ( - 1750)} }{2} [/tex]
and finally:
[tex]w1 = 50 \\ w2 = - 35[/tex]
since the width cannot be a negative number, w1 is the width, hence 50 ft, and the length is 65ft
