The area of the wings of a small Cessna is 175 ft2. If the length is 30 ft longer than the width, what are the dimensions of the wings? (This wing is one piece and goes along the top of the aircraft.)
my answer:
175 feet and the length is 30 ft longer and I looked through all the possible multiplication factors of 175
1,5,7,25,35,175,
the answer is got are 5 and 35
is length is 35 and width is 5?
Not enough information.
Are we supposed to know the geometrical shape of the wing?
Is is a rectangle?
Is it a trapezoid?
???
If it is a rectangle then you are correct, except your method of solving
is rather primitive. What is the area had been 174 ft^2 ?
to find the area the wings of a small Cessna:
www.boldmethod.com/images/learn-to-fly/aircraft-systems/wing-washout/root-stall.jpg
To find the dimensions of the wings, we can set up a system of equations using the given information.
Let's assume the width of the wings is "x" feet.
According to the given information, the length of the wings is 30 feet longer than the width. So, the length would be "x + 30" feet.
The area of the wings can be calculated by multiplying the length and width:
Area = Length × Width
175 = (x + 30) × x
To solve this equation, we can expand it:
175 = x^2 + 30x
Rearranging the equation into a quadratic form:
x^2 + 30x - 175 = 0
Now we need to solve this quadratic equation to find the possible values of "x" (width).
Using factoring, completing the square, or the quadratic formula, we find that the possible values for "x" are -35 and 5.
Since dimensions cannot be negative, we discard the negative value. Therefore, the width of the wings is 5 ft and the length is 30 ft longer, which is 5 + 30 = 35 ft.
So, the dimensions of the wings are:
Width = 5 ft
Length = 35 ft
To find the dimensions of the wings, we need to solve a system of equations based on the given information. Let's assume the width of the wings is x ft.
From the given information, we know that the length is 30 ft longer than the width. So, the length would be x + 30 ft.
The area of the wings is given as 175 ft^2. The formula for the area of a rectangle is length multiplied by width, so we can set up the equation:
x * (x + 30) = 175
Expanding this equation gives us:
x^2 + 30x = 175
Rearrange the equation to get it in standard quadratic form:
x^2 + 30x - 175 = 0
Now, we can solve this quadratic equation. One way is to factorize it. We need to find two numbers that add up to 30 and multiply to -175. After trying different pairs, we find that the factors -5 and 35 satisfy these conditions.
So, we can rewrite the equation as:
(x - 5)(x + 35) = 0
Setting each factor equal to zero, we get two possible solutions:
x - 5 = 0 or x + 35 = 0
Solving for x, we find that x = 5 or x = -35.
Since we're dealing with the dimensions of the wings, which cannot be negative, we discard the solution x = -35.
Therefore, the width of the wings is x = 5 ft.
And since the length of the wings is 30 ft longer than the width, the length would be 5 + 30 = 35 ft.
So, the dimensions of the wings are: width = 5 ft and length = 35 ft.