Geometry question form ax^2+bx+c

In summary, The question involves finding the areas and perimeter of four rectangles, with two variables (w and h) and a given equation for their sum (w + h = 25). The correct answer is C and an expression for the perimeter can be written as 2w + 2h = 50. The individual values of w and h are not necessary to determine in order to solve the problem.
  • #1
Daaniyaal
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I was tutoring a student and I came across the following question. I feel like I'm missing something obvious, but it seems like there are too many variables for an answer to be determined. The attached picture contains all of the question details.
 

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  • #2
The correct answer is C by the way
 
  • #3
Let w = width of the upper right rectangle, and
let h = height of the lower left rectangle.

Then the areas of the four rectangles, going clockwise from the upper left are a2, aw, ah, and 144.

What must the areas of the upper right and lower left rectangles add up to?
What's an expression that gives the perimeter?

I get C as the answer as well.
 
  • #4
aw+ah=25a
w+h=25

how do i determine the individual values of w and h?
 
  • #5
Daaniyaal said:
aw+ah=25a
w+h=25

how do i determine the individual values of w and h?
You don't have to. You have w + h = 25. Now write an expression for the perimeter.
 
  • #6
oh thanks! I got it :) I was missing the obvious >.<
 

1. What is the formula for solving a quadratic equation in the form ax^2+bx+c?

The formula for solving a quadratic equation in the form ax^2+bx+c is x = (-b ± √(b^2-4ac)) / 2a.

2. How do you determine the type of roots in a quadratic equation in the form ax^2+bx+c?

The type of roots in a quadratic equation in the form ax^2+bx+c can be determined by calculating the discriminant, which is b^2-4ac. If the discriminant is positive, the equation will have two real roots. If the discriminant is zero, the equation will have one real root. If the discriminant is negative, the equation will have two complex roots.

3. Can a quadratic equation have more than two solutions?

No, a quadratic equation can only have a maximum of two solutions. This is because it is a polynomial of degree 2, meaning it can have a maximum of two roots.

4. How do you graph a quadratic equation in the form ax^2+bx+c?

To graph a quadratic equation in the form ax^2+bx+c, you can plot points by substituting different values for x into the equation and solving for y. Alternatively, you can use the vertex form of the equation, which is y = a(x-h)^2 + k. The vertex of the parabola will be at the point (h,k) and you can plot points on either side of the vertex to create a symmetrical curve.

5. What is the difference between a quadratic function and a quadratic equation?

A quadratic function is a mathematical expression that contains a variable squared, while a quadratic equation is an expression that sets the function equal to zero. In other words, a quadratic function is a type of equation, but not all equations are quadratic functions.

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