SOLUTION: A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 16 16 feet more than the length of the shortest side. Find t

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Question 1149873: A flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is
16
16 feet more than the length of the shortest side. Find the dimensions if the perimeter is
172
172 feet.
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

x + 2x + (x+16) = 172


4x = 172 - 16 = 156


    x = 156/4 = 39 feet is the length of the shortest side.


Hence, according to the condition, the sides of the triangle shoud be 39, 2*39 = 78 and (39+16) = 55 feet long.    ANSWER

Since the triangle inequalities are satisfied, such a triangle really does exist.

It completes the solution.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

A flower bed is in the shape of a triangle: so, the perimeter is
P=a%2Bb%2Bc where a is the shortest side, and b is other side twice the length of the shortest side and the third side c is 16 feet more than the length of the shortest side.
so, sides are:
a
b=2a
c=a%2B16
Find the dimensions if the perimeter is 172 feet.
given:
P=172, a, b=2a,c=a%2B16

so, we have
172=a%2B2a%2Ba%2B16 .........solve for a

172=4a%2B16

172-16=4a

156=4a

156%2F4=a

a=highlight%2839%29->the shortest side

b=2a->b=highlight%2878%29->other side

c=a%2B16->c=39%2B16->c=highlight%2855%29->the third side

check the perimeter:
172=a%2Bb%2Bc
172=39%2B78%2B55
172=172