Question

Help Please
A right triangle has base (x - 6) units and height (6x - 12) units.

Part A: What is the square of the length of the hypotenuse of the triangle? Show your work.

Part B: What is the area of the triangle?

Part C: Using the solution obtained in Part B, explain the closure property of multiplication of polynomials.

Answer 1

im guessing you have to square (x-6)^2 and (6x-12)^2

Answer 2

am i right

Answer 3

and then for part b i solve it right

Answer 4

tell me if im wrong please

Answer 5

anyone

Answer 6

know

Answer 7

help please

Answer 8

Part A wants the length of the hypotenuse in squared form. Do you know how to find the length of the hypotenuse when you know the length of the other two sides?

Answer 9

no

Answer 10

sorry

Answer 11

Yes, you're right. For part B, the answer I get it 6 *sqrt (x-2)^2 + (x-6)^2 = c

Answer 12

\[a^2 + b^2 = c^2\]

Answer 13

We need c^2

Answer 14

ok how do i do that

Answer 15

Ok, well in this case we know the value of the base and the height, so it would look like this:

Answer 16

im confused

Answer 17

i dont see anything

Answer 18

Ok, do you know what a hypotenuse of a triangle is?

Answer 19

no

Answer 20

It's the longest side of a right triangle. It's also a right triangle because it has a 90 degree angle.

Answer 21

ok so do i have to take the height and square it

Answer 22

so (6x-12)^2

Answer 23

\[a^2 + b^2 = c^2\]

We have to square the height, and add it to the square of the base.

Answer 24

so (x-6)^2+(6x-12)^2

Answer 25

Yep, now when you simplify that don't remove the square.

Answer 26

ok so how do i simplify

Answer 27

sorry ive been testing for 5 hours my brains kind of fried

Answer 28

so do i do the foil method

Answer 29

You would use the foil method if this was a quadratic we were going to simplify, but that's actually completely unrelated

Answer 30

\[(x - 6)^2 + (6x - 12)^2 = c^2\]

First we should simplify the x values

Answer 31

What is x + 6x?

Answer 32

6x^2

Answer 33

That would be 6x * x

Answer 34

\[x + x = 2x\]

\[x * x = x^2\]

Answer 35

oh then im not sure sorry

Answer 36

is it 7x or 8x

Answer 37

for x + 6x, remember that there's actually a hidden 1 beside the x.

1x + 6x = 7x

Answer 38

oh ok thanks

Answer 39

Now -6 - 12 simplified is

Answer 40

-18

Answer 41

so for part A:

\[c = (7x - 18)^2\]

Answer 42

thanks

Answer 43

so what do i do for b

Answer 44

For part B we need the area of the triangle

The formula for the area of a right triangle is:

\[\frac{ ab }{ 2 }\]

Answer 45

And again:

A = x - 6
B = 6x - 12

Answer 46

ok so i have to solve for x

Answer 47

Yep, I think I can see some foiling up ahead

Answer 48

ok so what do i have to foil

Answer 49

oh wait never mind its A = x - 6
B = 6x - 12 that i have to foil right

Answer 50

\[Area = \frac{ ab }{ 2 }\]

\[Area =\frac{ (x - 6)(6x - 12) }{ 2 }\]

Answer 51

The binomial on top should be turned into a quadratic I believe

Answer 52

ok so would be

Answer 53

im trying to draw it

Answer 54

so the second part would be (3x-6)

Answer 55

but for the first it would be (?-3) im not sure what x/2 is

Answer 56

Firs just foil (x−6)(6x−12)

Answer 57

oh ok

Answer 58

so the same as before

Answer 59

(7x-18)just not squared this time

Answer 60

The other time we added them together, this time we're multiplying.

Do you know the steps to foiling?

Answer 61

oh yeah i understand

Answer 62

so

Answer 63

(6x^2 am i starting out right

Answer 64

That was also my first term

Answer 65

ok so for the rest is it x times 12 or -12

Answer 66

For the outers it's x * (-12)

Answer 67

ok so what would that be im always confused when it comes to multiplying x

Answer 68

what it be -12x

Answer 69

-12x would be correct

Answer 70

So now should be the inners

Answer 71

ok so (6x^2-(-12)9-36-72)

Answer 72

oops i made an error

Answer 73

(6x^2-(-12)(-36-72)

Answer 74

When simplified I got:\[6x^2 - 48x + 72\]

Answer 75

i so i did it wrong where did i mess up

Answer 76

I think there was a problem with the positives and negatives of 12 and 72

Answer 77

oh ok so the final answer is 3x^2-42x+36

Answer 78

i mean 24

Answer 79

3x^2-24x+36

Answer 80

Yep, so I'll just re-write it:

Answer 81

\[3x^2 - 24x + 36\]

Answer 82

First of all do you recognize what type of expression this is?

Answer 83

no

Answer 84

This is a quadratic because the highest power is 2