SOLUTION: I've been working on this all day. And i need some assistance. Can someone please help me? A right triangle has legs of lengths 9 and 12 (a) Its hypotenuse has a length of_____

Algebra ->  Pythagorean-theorem -> SOLUTION: I've been working on this all day. And i need some assistance. Can someone please help me? A right triangle has legs of lengths 9 and 12 (a) Its hypotenuse has a length of_____      Log On


   

Question 85405: I've been working on this all day. And i need some assistance. Can someone please help me?
A right triangle has legs of lengths 9 and 12
(a) Its hypotenuse has a length of_______
(b) The altitude to the hypotenuse divides it into segments of lengths___ and ____
(c) The altitude to the hypotenuse has length_____
Found 2 solutions by Nate, jim_thompson5910:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
I've been working on this all day. And i need some assistance. Can someone please help me?
A right triangle has legs of lengths 9 and 12
(a) Its hypotenuse has a length of_______
a^2 + b^2 = c^2
a is a side
b is the other side
c is the hypotenuse
9^2 + 12^2 = c^2
81 + 144 = c^2
225 = c^2
15 = c
(b) The altitude to the hypotenuse divides it into segments of lengths___ and ____
The altitude strikes the hypotenuse at a right angle. Assume the larger length of the hypotenuse is x and the smaller portion is 15 - x. Knowing your theorm, you should get:
12^2 = (x)15
9.6 = x
You have the lengths: x and 15 - x
You have the lengths: 9.6 and 5.4
(c) The altitude to the hypotenuse has length_____
Knowing your theorm:
h^2 = 9.6 * 5.4
h = 7.2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we have a triangle with legs of 9 , 12 and a hypotenuse of x(our unknown side), we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
a%5E2%2Bb%5E2=c%5E2

9%5E2%2B12%5E2=c%5E2 Plug in a=9 and b=12 and lets solve for c
8+1+%2B+1+4+4+=++c++%5E+2 Square each individual term



2+2+5+=++c++%5E+2 Combine like terms


s+q+r+t+%28+2+2+5+%29+=+s+q+r+t+%28++c++%5E+2+%29 Take the square root of both sides


1+5+=+c Simplify



So our answer is
c+=+1+5

(a) "Its hypotenuse has a length of__15__"


To find the altitude (to the hypotenuse), we can use this formula:

Altitude=a%2Ab%2Fc

Altitude=9%2A12%2F15=108%2F15=7.2 plug in the given info

So the length of the altitude is 7.2
(c) The altitude to the hypotenuse has length___7.2__"



So now construct a smaller triangle within the given one. Now using the altitude's length, we can find one piece of the hypotenuse

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Since we have a triangle with legs of x (our unknown side), 7.2 and a hypotenuse of 9, we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
a%5E2%2Bb%5E2=c%5E2

a%5E2%2B7.2%5E2=9%5E2 Plug in b=7.2 and c=9 and lets solve for a
+a++%5E+2+%2B+51.84+=+8+1 Square each individual term



+a++%5E+2+=+8+1+-+51.84 Subtract 51.84 from both sides


+a++%5E+2+=+29.16 Combine like terms


s+q+r+t+%28++a++%5E+2+%29+=+s+q+r+t+%28+29.16%29 Take the square root of both sides


a+=+5.4 Simplify

So our answer is
a+=+5.4

So the length of one piece of the hypotenuse is 5.4. Now subtract 5.4 from 15 to find the other piece's length

15-5.4=9.6

So the length of the other piece is 9.6

(b) The altitude to the hypotenuse divides it into segments of lengths_5.4__ and _9.6___