Question

A right triangle has base (x - 5) units and height (4x - 10) 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

Because it's a right triangle, you can use the Pythagorean theorem - a^2 + b^2 = c^2. You have a (x-5) and b (4x-10) - from there, you need to find c (for part a)

Answer 2

so I multiply a and b to get c to solve part A?

Answer 3

a squared and b squared multiplied will give you c squared - simply a times b will not give you a correct answer.

Answer 4

so for part a what would i need to do?

Answer 5

you need the product of a^2 and b^2 - so find that, and you'll have c^2. From there, how do you find c?

Answer 6

im not really sure

Answer 7

can you explain how?

Answer 8

another way to phrase the theorem is a*a + b*b = c*c . Does that make it clear?

Answer 9

yes. I understand the pythagorean theorem but what I don't understand is when I get c^2, is that my answer for part a?

Answer 10

no, you need to take the square root of c^2 to get c, and that will be your answer for part a.

Answer 11

"A right triangle has base (x - 5) units and height (4x - 10) units." If you square the two given dimensions (which represent the lengths of the two sides of the triangle), and then add them together, the result is the answer you want. Please review the original question.

Answer 12

"What is the square of the length of the hypotenuse of the triangle? " You want c^2, not c.

Answer 13

So you had the cprrect answer all along.

Answer 14

So this is how i would do it:
a^2 + b^2 = c^2
(x-5)^2 + (4x-10)^2
x^2 - 10 + 25 + 16x^2 - 80x + 100

Answer 15

Is this right so far?

Answer 16

Thanks for sharing your work. Wouldn't that 2nd term be -10x, not just -10?
Otherwise you're right on track.

Answer 17

your right, sorry I didn't realize that. ANd after that I add them to get c^2?

Answer 18

Combine like terms, and then you'll be done with Part A.

Answer 19

Combine would be a better term here than Add.

Answer 20

Or, Simplify.

Answer 21

Part B: You are given both the base and the height of this triangle. What's the formula for the area of a triangle, when such info is given?

Answer 22

x^2 - 10x + 25 + 16x^2 - 80x + 100
17x^2 - 90x +125
Is this right?

Answer 23

the formula would be base times height so I would multiply (x - 5)(4x - 10)?