SOLUTION: how many different triangles,if any, can be drawn with one 90 degree angle and side lengths of 5 cm. and 12 cm?

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Question 739430: how many different triangles,if any, can be drawn with one 90 degree angle and side lengths of 5 cm. and 12 cm?
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
2 triangles
(1)
the legs can be 5 cm and 12 cm
+h%5E2+=+5%5E2+%2B+12%5E2+
+h%5E2+=+25+%2B+144+
+h%5E2+=+169+
+h+=+13+
The hypotenuse is 13 cm
(2)
The hypotenuse can be 12 cm and
one of the legs can be 5 cm
+12%5E2+=+5%5E2+%2B+b%5E2+
+b%5E2+=+144+-+25+
+b%5E2+=+119+
+b+=+10.99087+
-----------------
The other choice with hypotenuse = 5 cm
and a leg = 12 cm is impossible. There is no
way to make a right angle with the other leg

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
one 90 degree angle and
side lengths of 5cm and 12cm

A right isosceles triangle has a 90-+45-+45 degree angles.
Another interesting right triangle is the 30-60-90 degree triangle. The ratio of this triangle's longest side to its shortest side is "two to one." That is, the longest side is twice as long as the shortest side.
One of the most famous is the "3, 4, 5 triangle."


However, the Pythagorean Theorem can help us to find third side if given side lengths of 5cm and 12+cm


assume that 12+cm is hypotenuse c and 5cm is leg a

c%5E2=a%5E2%2Bb%5E2
12%5E2=5%5E2%2Bb%5E2
144=25%2Bb%5E2
144-25=b%5E2
119=b%5E2
10.9087=b.........this cannot be solution

let’s assume that 12cm is leg a and 5cm is leg b
c%5E2=a%5E2%2Bb%5E2
c%5E2=12%5E2%2B5%5E2
c%5E2=144%2B25
c%5E2=169
c=13.....this is solution
so, you can draw one triangle with one 90 degree angle and
sides lengths of 5cm,12cm, and 13cm