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. (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. (3 points)

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Answer 1

hypotenuse^2 = base^2 + height^2

Answer 2

Use the Pythagorean theorem to find the hypotenuse. You know the two sides.

a = x-5
b = 4x-10
c is hypotenuse

a^2 + b^2 = c^2

So square a, square b, add them together and take the square root. The result is c, the length of the hypotenuse.

To find the area of a triangle, multiply 1/2 times the base times the height.

Answer 3

area = (1/2) base x height