SOLUTION: How can I find the perimeter of a triangle if only one side is given and the hypotenuse is 3 cm longer than the unknown side. Is that possible if there is no value given for the pe

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Question 1080035: How can I find the perimeter of a triangle if only one side is given and the hypotenuse is 3 cm longer than the unknown side. Is that possible if there is no value given for the perimeter? The question reads: Hypotenuse of a right triangle is 3cm longer than one leg. The other leg is 9cm, find the perimeter of the triangle.
so P= x +(x+3)+9
or to try and solve for the other side
a^2 +b^2 = c^2

so
9^2 + x^2 = (x+3)^2
I can't figure out how I can solve for a perimeter that is unknown when two sides are also unknown. Is it possible? Thanks?

Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're on the right track. Nice work so far.

Let's solve for x

9%5E2+%2B+x%5E2+=+%28x%2B3%29%5E2

81+%2B+x%5E2+=+%28x%2B3%29%28x%2B3%29

81+%2B+x%5E2+=+x%28x%2B3%29%2B3%28x%2B3%29 Distribute

81+%2B+x%5E2+=+x%5E2%2B3x%2B3x%2B9 Distribute again

81+%2B+x%5E2+=+x%5E2%2B6x%2B9

81+%2B+x%5E2-x%5E2+=+x%5E2%2B6x%2B9-x%5E2 Subtract x^2 from both sides

81+=+6x%2B9

81-9+=+6x%2B9-9 Subtract 9 from both sides

72+=+6x

6x+=+72

6x%2F6+=+72%2F6 Divide both sides by 6 to isolate x

x+=+12

So the other leg is 12 cm and the hypotenuse is 15 cm (since it's 3 cm longer than the previously unknown leg).

The perimeter is therefore:

P = a+b+c

P = 9+12+15

P = 36

Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your equation is


9%5E2+%2B+x%5E2 = %28x%2B3%29%5E2.


where x is "the other leg".


Can you solve it ?


When you solve it, find the hypotenuse as sqrt%289%5E2%2Bx%5E2%29  or simply as (x+3) (it is the same).


Then find the perimeter as the sum of the two legs and the hypotenuse.


If you want to see a variety of solved similar sample problems, look into the lessons
    - Solved problems on the perimeter and side lengths of a triangle
    - Solved problems on the perimeter and side lengths of a right-angled triangle
    - Solved problems on the perimeter and the side lengths of a parallelogram
    - Solved problems on the perimeter and side lengths of a rectangle
in this site that are specially prepared for students like you.


Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Finding the perimeter and sides lengths of triangles, parallelograms, rectangles and polygons".