A piece of wire is to be bent into a triangle such that the shortest side is 5 inches less than the second side, and the longest side is twice the shortest side. If the piece of wire is 45 inches long, what is the length of each side of the triangle?

2 Answers
Feb 17, 2018

I tried this:

Explanation:

Consider the diagram:
enter image source here
The Perimeter #P# will be:
#P=a+b+c=45#
and:
#c=a+5#
#b=2a#
let us substitute these last into the perimeter:
#a+2a+a+5=45#
so that:
#4a=40#
#a=40/4=10"in"#
and:
#b=2a=20"in"#
#c=a+5=10+5=15"in"#

Feb 17, 2018

#10, 15" and "20" inches"#

Explanation:

#"let the shortest side "=x#

#"then the second side "=x+5#

#"and the third side "=2x#

#"now perimeter "=45#

#rArrx+x+5+2x=45#

#rArr4x+5=45#

#"subtract 5 from both sides"#

#4xcancel(+5)cancel(-5)=45-5#

#rArr4x=40#

#"divide both sides by 4"#

#(cancel(4) x)/cancel(4)=40/4rArrx=10#

#color(blue)"the lengths of the sides of the triangle are"#

#x=10, x+5=15" and "2x=20#

#rArr10,15" and "20" inches"#