Question

Can someone please help me? I have no idea how to figure this out.
Part A ~ The area of a triangle is (9x^2 - 12x + 4) square units. determine the length of each side by the square factoring the area expression completely. Show your work.
Part B ~ The area of a rectangle is (25x^2 - 16y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.
Part C ~ The volume of a rectangular box is (x^3 - 7x^2 - 9x + 63) cubic units. determine the dimensions of the rectangular box by factoring the volume expression completely. Show your w

Answer 1

The area of a triangle of height h and base b is A = (1/2)*b*h.
In this case the area is given and is (9x^2-12x+4), which must equal (1/2)*b*h.

Start by factoring the expression on the left. Equate the factors to (1/2)*b*h. What do you think the values of a and b are? (They're algebraic expressions, not numerals.)

Answer 2

Well if they're algebraic expressions, then they wouldn't have a value.

Answer 3

@Diego98512 ... You would happen to be a math genus too, would you? :P

Answer 4

So uhh, whatcha need to do is uhh..... @BVB4rmy halp?

Answer 5

Please factor: 9x^2-12x+4

Answer 6

It's (3x^2)^2

Answer 7

Better check those factors. But you're on the right track.

Answer 8

Whoops. It's (3x - 2) (3x - 2) or (3x - 2)^2

Answer 9

Right. Then equate this to A = (1/2)*(base)(height):

A = (1/2) (base) (height) = (3x - 2) (3x - 2). Multiply the right side by (2/2) and then re-arrange the result so that it appears like (1/2) (base) (height).

Answer 10

You'd get
9x2−15x+6

Answer 11

The point of this problem was to come up with expressions for the length and the width of the given triangle, whose area is 9x^2 - 12x + 4.

9x^2 - 12x + 4 = (3x - 2) (3x - 2) = (1/2) (base) (height).

One way of doing this would be to write A = (1/2) (base) (height) = \[\frac{ 2(3x - 2)*(3x -2) }{ 2 } = \frac{ 1 }{ 2 }*[2*(3x-2)]*(3x-2).\]

Answer 12

You could now say that (base)=2(3x-2) and height = (3x-2, or vice versa.

Answer 13

Oh ok. Now what am i supposed to do to find the dimensions in part B?

Answer 14

Think about what you did in Part A. Mind explaining this, briefly...what did you do to obtain the dimensions of the triangle?

Part B is easier than Part A, because all you really need to do is to factor the algebraic expression given. Its factors represent the length and width of the rectangle. Can you figure out which one is the length and which one is the width?

Answer 15

I actually finished it already. Thanks for all your help! :D