Question

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. (4 points)
Part B: What is the area of the triangle? (3 points)
Part C: Using the solution obtained in Part B, explain the closure property of multiplication of polynomials.

Answer 1

A. Pythagoras: h^2 = a^2 + b^2
B. Area = (1/2)(base)(height)
C. beats me!

Answer 2

Part A (6x-12)^2 + (x - 6)^2
(36x^2 - 144x +144) + (x^2 - 12x + 36)
Combine like terms and that is Part A.

Answer 3

\[37x ^{2}-156x+180\]

Answer 4

So Is that the answer for A? Or do you have to simplify it more?

Answer 5

Should that not be the square root of 37x^2-156X+180?

Answer 6

what do you mean?

Answer 7

a. asks for the square
b. asks for the area

Answer 8

Sorry, I was out. No that is simplified enough, and the problem was asking for the "square" as @douglaswinslowcooper stated in his post above.
Part B is asking for the area. The area A of a triangle is A=(1/2)bh where b is base and h is height. Refer to diagram above A=(1/2)(x-6)(6x-12)
simplify by taking 1/2 of the height h getting (3x-6) now multiply (x-6)(3x-6) getting:
3x^2 - 24x + 36 sq units (as it is area.)

Answer 9

Part C. Just show that the multiplication of two polynomials (x-6)(3x-6) results in a polynomial 3x^2 - 24x + 36 as a result of the distributive process and combing of similar terms.