SOLUTION: The length of the sides of a triangle are in the ratio Of 17:10:9. Find the lengths of the three sides If the area of the triangle is 576 square cm.

Algebra ->  Triangles -> SOLUTION: The length of the sides of a triangle are in the ratio Of 17:10:9. Find the lengths of the three sides If the area of the triangle is 576 square cm.      Log On


   

Question 1119647: The length of the sides of a triangle are in the ratio
Of 17:10:9. Find the lengths of the three sides
If the area of the triangle is 576 square cm.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The length of the sides of a triangle are in the ratio
Of 17:10:9. Find the lengths of the three sides
If the area of the triangle is 576 square cm.
---------
Find the area of a triangle with sides 17, 10 & 9
---
Using Heron's Law:
Area = sqrt(18*1*8*9) = sqrt(1296) = 36
576/36 = 16
sqrt(16) = 4
--> sides are 68, 40 and 36

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The key to this problem is to find the area of a general triangle when the measures of three sides are known. Use Heron's formula:



Where are the measures of the three sides and is the semiperimeter:

Since you are given the ratio of the sides the actual measures of the sides can be expressed as .



Then



Which is given to be equal to

Solve for and then calculate


John

My calculator said it, I believe it, that settles it