Answer
Length = $35$ ft
Width = $5$ ft
Work Step by Step
First, we can say that the width of the wing is represented by $x$, and the length can then be expressed as $(x+30)$ ft as it is $30$ ft longer than the width.
So, now we know that:
Length = $(x+30)$ ft
Width = $x$ ft
Area = $175 ft^2$
We also know that the formula for the area of a rectangle is Length × Width.
Using this formula, we can substitute the values mentioned earlier to form a quadratic equation.
Area = Length × Width
$175=(x+30)×x$
$175=x^2+30x$ (Subtract 175 from each side to make the equation=0)
$x^2+30x−175=0$
Now that we have our equation, we can solve it by factoring!
$x^2+30x−175=0$
$x^2+35x-5x−175=0$
$x(x+35)-5(x+35)=0$
$(x-5)(x+35)=0$
We can make each bracket = 0 to find the solutions for $x$.
$(x-5)=0$ or $(x+35)=0$
$x=5$ or $x=-35$
Since we are finding the width of a rectangle, it cannot be negative as the width cannot be below 0. So, $x=5$.
Length = $(5)+30$
= $35$ ft
Width = $5$ ft
