Hi, there--
THE PROBLEM:
One side of a triangle is 6 meters more than twice the shortest side. The third side is 9 meters more than
the shortest side. The perimeter is 75 meters. Find all the sides.
A SOLUTION:
Let A be the shortest side.
One side is 6 meters more than twice the shortest side. Twice the shortest side is 2A.
Six more than 2A is 2A + 6
The third side is 9 meters more than the shortest side, or A + 9.
The perimeter is the sum of the all three side lengths, or 75 meters. So
A + 2A + 6 + A + 9 = 75
Combine the like terms: A+2A+A is 4A and 6+9 is 15.
4A + 15 = 75
Subtract 15 from both sides to isolate the variable.
4A + 15 - 15 = 75 - 15
4A = 60
Divide both sides of the equation by 4 to get the variable alone on the left. (4A/4 is A.)
4A/4 = 60/4
A = 15
In the context of this problem A = 15 means that the shortest side is 15 meters.
One side is 6 more than twice 15, or 36 meters.
The third side is 9 meters more that 15, or 24 meters.
The perimeter is 15 + 24 + 36 = 75 meters.
Hope this helps! Feel free to email if you have any questions about the solution.
Good luck with your math,
Mrs. F
math.in.the.vortex@gmail.com
