SOLUTION: 4. A triangle has sides that are 12 cm, 15 cm and 20 cm in lengths. Classify it as acute, obtuse or right or say there is insufficient information.

Algebra ->  Pythagorean-theorem -> SOLUTION: 4. A triangle has sides that are 12 cm, 15 cm and 20 cm in lengths. Classify it as acute, obtuse or right or say there is insufficient information.      Log On


   



Question 1114733: 4. A triangle has sides that are 12 cm, 15 cm and 20 cm in lengths. Classify it as acute, obtuse or right or say there is insufficient information.
Found 3 solutions by ikleyn, greenestamps, josgarithmetic:
Answer by ikleyn(52752) About Me  (Show Source):
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


If c is the longest side of a triangle and the other two sides are a and b, then

(1) if c%5E2+=+a%5E2%2Bb%5E2 then the triangle is a right triangle;
(2) if c%5E2+%3E+a%5E2%2Bb%5E2 then the triangle is obtuse;
(3) if c%5E2+%3C+a%5E2%2Bb%5E2 then the triangle is acute.

For the given lengths,
c%5E2+=+400
a%5E2%2Bb%5E2+=+144%2B225+=+369

c%5E2+%3E+a%5E2%2Bb%5E2 so the triangle is obtuse.

Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
12, 15, 20
3*4, 3*5, 5*4


12%5E2%2B15%5E2versus20%5E2

144%2B225versus400

369%3C400
Obtuse