)a triangle measures 6 inches by 8 inches by 9 inches. is this triangle a right, obtuse, or acute triangle? why?

c^2 < a^2 + b^2 = acute

c^2 >  a^2 + b^2 = obtuse

c^2 =  a^2 + b^2 = right

so 

9^2 = 81

6^2 + 8^2 = 36 + 64 = 100

81<100

So the triangle is an acute triangle

Hope it helps

what is the original number? you forgot to add it.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240