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Define the three sides to be a,b,c such that a < b < c
So c is the longest side, and 'a' is the shortest with b in the middle.
"longest side is 4 ft shorter than twice the shortest side" means that c = 2a-4
"third side is 3 ft longer than the shortest side" so b = a+3
Both b and c are in terms of 'a', allowing us to do substitutions like so
a+b+c = perimeter
a+b+c = 59
a+(a+3)+c = 59 .... first substitution, plug in b = a+3
a+(a+3)+(2a-4) = 59 ... second substitution, plug in c = 2a-4
4a-1 = 59 .... combine like terms
4a = 59+1 ... add 1 to both sides
4a = 60
a = 60/4 ... divide both sides by 4
a = 15
The shortest side is 15 ft
b = a+3 = 15+3 = 18
The middle side is 18 ft
c = 2a-4 = 2*15-4 = 26
The longest side is 26 ft
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Check:
The three sides should add up to a perimeter of 59 ft
a+b+c = 15+18+26 = 59
so the answer is confirmed
Answer:
[tex]Leg_1 = 15\\Leg_2 = 26\\Leg_3 = 18[/tex]
Step-by-step explanation:
Form an equation.
[tex](x)+(2x-4)+(x+3)=59[/tex]
Combine like terms.
[tex]4x-1=59[/tex]
Add 1 to both sides, then divide both sides by 4.
[tex]4x=60\\\\\frac{4x}{4}=\frac{60}{4}\\\\x = 15[/tex]
Plugin in 15 for x
[tex]Leg_1 = 15\\Leg_2 = 2(15)-4=26\\Leg_3 = 15 + 3=18[/tex]
