Question

Your friend comes up with a design for the perfect garden and says to create it you need an area of 35 square feet. if this is your ideal garden, what would be the measurements of your width and length

Answer 1

This has a many multitude of possibilities

Answer 2

you solve with a quadratic equation if that helps!

Answer 3

First, the equation of an area: A= w*l, where "w" is width and "l" is length.

So we have 35 = w*l. In other words, think of two numbers that when multiplied together equals 35!

Answer 4

5 and 7?

Answer 5

That'll work. That way, you get an area of 35. Specifically it should be 5ft and 7ft if your teacher is really into that.

Answer 6

how do i show it on a Quad equation?

Answer 7

also, the second part of the question is….during the winter months, MR Dugan assigns another set of students to design a rectangular tent to cover your garden. the volume of their tent was represented by 2x^2-5x^2+3x. the garden still had the original length and width from the previous example, what was the measure of height in terms of x

Answer 8

^ second part involves factoring

Answer 9

Well, if you need to use a quadratic equation, it changes things. One, it ensures the garden has to be a square. Because it's a square, all the sides are equal, in other words, w = l. So, 5ft and 7ft are no longer acceptable answers.

Answer 10

wow youre awesome… i didnt even realize… how do i go about it now

Answer 11

So, you now have the w^2 (or l^2. I'm using w). so w^2 = A.

The quadratic equation is ax^2 + bx + c = 0. 'x' typically represents the unknown, which in this case will be 'w' (keep in mind that a ≠ A). So aw^2 + bw + c = 0.

If the original area equation is w^2 = 35, we need to alter it to match the quadratic formula. First, we subtract 35 from both sides. This gets us

w^2 - 35 = 0

So then c has to be -35. So what to a and b have to be to match that equation?

Answer 12

Also, keep in mind that since this is something in the real world, w CANNOT be negative. Otherwise your ideal garden wouldn't exist.

Answer 13

so do you find the square root of 35 for the answer

Answer 14

Seems so. Using the quadratic equation seems really roundabout though.

Answer 15

okk i will just do that… do you know how to do part two?? ….during the winter months, MR Dugan assigns another set of students to design a rectangular tent to cover your garden. the volume of their tent was represented by 2x^2-5x^2+3x. the garden still had the original length and width from the previous example, what was the measure of height in terms of x

Answer 16

using factoring

Answer 17

Alright so we have the volume of a rectangle being (w*l*h). The equation given for the prism is 2x^2 - 5x^2 +3x. First things first, simplify it a little to -3x^2 + 3x.

So the two volumes have to equal each other, right? so -3x^2 + 3x = (w*l*h)

As we discovered in question 1, w (and by default l) equal sqrt(35). So it should be -3x^2 + 3x = (35 * h), making it 3x^2 + 3x = 35h. In quadratic terms, it's -3x^2 + 3x -35h = 0

Answer 18

You can't factor with h in the equation though, so you have to move it back. All factoring really does here is simplify the equation. So what do -3x*x and 3*x have in common? Take whatever they have in common out and see what remains.

Don't forget to make sure h is alone at the end.