Question

the perimeter of a triangle is 71 feet. one side is 11 feet longer than the base while the longest side is 19 feet longer than the base. find the length of the longest side.
you do not need to include the unit measurement or unit type. only the numerical answer is necessary. round to the nearest tenth if necessary.

Explanation:

Step1: Let the base length be \(x\)

Let the base of the triangle be \(x\) feet. Then one side is \(x + 11\) feet and the longest side is \(x+19\) feet.

Step2: Use the perimeter formula

The perimeter of a triangle \(P=a + b + c\). Here \(P = 71\), \(a=x\), \(b=x + 11\), \(c=x + 19\). So \(x+(x + 11)+(x + 19)=71\).
Simplify the left - hand side: \(3x+30 = 71\).
Subtract 30 from both sides: \(3x=71 - 30=41\).
Divide both sides by 3: \(x=\frac{41}{3}\).

Step3: Find the length of the longest side

The longest side is \(x + 19\). Substitute \(x=\frac{41}{3}\) into \(x + 19\): \(\frac{41}{3}+19=\frac{41+57}{3}=\frac{98}{3}\approx32.7\)

Answer:

\(32.7\)