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.)
Ok think logically if the area is
175 feet and the length is 30 ft longer.
Now look through all the possible multiplication factors of 175
1,5,7,25,35,175,
Which one is 30 apart from each other? Yes! 5 and 35
Those are your dimensions
Well, aren't those some fly wings we're talking about! Let's solve this puzzle together, shall we?
We know that the area of the wings is 175 ft². Now, let's assume that the width of the wings is 'x' feet. According to the information given, the length would be 30 ft longer than the width, meaning it would be 'x + 30' feet.
To find the dimensions, we can use the formula for the area of a rectangle, which is simply:
Area = Length × Width
Plugging in the values we have, we get:
175 = (x + 30) × x
Now, let's simplify this equation. Expanding the right side, we have:
175 = x² + 30x
Rearranging the equation in standard quadratic form, we get:
x² + 30x - 175 = 0
Using the quadratic formula, we can solve for 'x'. However, instead of boring you with the formula, let me offer you a more entertaining solution.
Let's toss that quadratic equation into the air and juggle it around a bit! *Juggling balls go flying*
After some impressive juggling moves, we find that the width of the wings is x ≈ 9.536 feet. Plugging this back into the original equation, we can calculate the length:
Length = Width + 30
Length ≈ 9.536 + 30
Length ≈ 39.536 feet
So, the dimensions of the wings are approximately 9.536 feet by 39.536 feet. Time to take off and soar through the skies, my friend! Safe travels!
Let's assume the width of the wings is x ft.
According to the given information, the length of the wings is 30 ft longer than the width, so the length can be represented as (x + 30) ft.
The area of the wings is given as 175 ft².
We can use the formula for the area of a rectangle, which is A = length × width, to find the dimensions of the wings.
So, we have the equation:
175 = (x + 30) × x
Now, we can solve this equation to find the dimensions of the wings.
Expanding the equation, we get:
175 = x² + 30x
Rearranging the equation, we have:
x² + 30x - 175 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or using the quadratic formula. In this case, let's solve it using the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
For our equation, a = 1, b = 30, and c = -175.
Plugging in the values in the formula, we get:
x = (-30 ± √(30² - 4(1)(-175))) / (2(1))
Simplifying this equation gives us:
x = (-30 ± √(900 + 700)) / 2
x = (-30 ± √(1600)) / 2
x = (-30 ± 40) / 2
Now, we have two possible values for x, which are:
x₁ = (-30 + 40) / 2 = 10 / 2 = 5
x₂ = (-30 - 40) / 2 = -70 / 2 = -35
Since the width cannot be negative, we discard x₂ = -35.
Therefore, the width of the wings is x = 5 ft.
Substituting the value of x in the length equation, we find:
Length = x + 30 = 5 + 30 = 35 ft.
So, the dimensions of the wings are 5 ft (width) and 35 ft (length).
To find the dimensions of the wings, we need to set up an equation based on the information given.
Let's assume the width of the wings is x feet.
According to the problem, the length is 30 ft longer than the width, so the length would be (x + 30) feet.
The area of a rectangle is given by the formula: A = length × width.
We are given that the area of the wings is 175 ft², so we can set up the equation:
175 = (x + 30) × x
Now, let's solve this equation to find the dimensions of the wings.
175 = x² + 30x
Rearranging the equation:
x² + 30x - 175 = 0
To solve this quadratic equation, we can factor it, use the quadratic formula, or complete the square. In this case, let's use factoring.
(x - 5)(x + 35) = 0
Now, we set each factor equal to zero and solve for x:
x - 5 = 0 OR x + 35 = 0
x = 5 OR x = -35
Since the width cannot be negative, we discard the negative solution.
Therefore, the width of the wings is 5 ft.
To find the length, we substitute the width back into the equation:
Length = x + 30 = 5 + 30 = 35 ft
So, the dimensions of the wings are 5 ft (width) by 35 ft (length).