Question

The longest side of the triangle section is 4 feet shorter than twice the shortest side. The third side is 3 feet longer than the shortest side. The perimeter is 59 feet . How long is each side

Answer 1

Answers:

The shortest side is 15 ft

The middle side is 18 ft

The longest side is 26 ft

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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 2

Answer:

$Leg_1 = 15\\Leg_2 = 26\\Leg_3 = 18$

Step-by-step explanation:

Form an equation.

$(x)+(2x-4)+(x+3)=59$

Combine like terms.

$4x-1=59$

Add 1 to both sides, then divide both sides by 4.

$4x=60\\\\\frac{4x}{4}=\frac{60}{4}\\\\x = 15$

Plugin in 15 for x

$Leg_1 = 15\\Leg_2 = 2(15)-4=26\\Leg_3 = 15 + 3=18$