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

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)   (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

Distribute

Distribute again

Subtract x^2 from both sides

Subtract 9 from both sides

Divide both sides by 6 to isolate x

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(52890)   (Show Source): You can put this solution on YOUR website!
.

Your equation is = . where x is "the other leg". Can you solve it ? When you solve it, find the hypotenuse as 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".

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