Question

find the value of t.
1 mi
t
t
5 mi
perimeter = 14 miles
t = miles

Explanation:

Step1: Write the perimeter formula

The perimeter \(P\) of a trapezoid is \(P=a + b+ c + d\). In this isosceles trapezoid (since the non - parallel sides are equal, \(c = d=t\), \(a = 1\) mi, \(b = 5\) mi, and \(P=14\) mi). So, \(P=1 + 5+t + t\).

Step2: Simplify the equation

Simplify \(1 + 5+t + t\) to \(P=6 + 2t\). Substitute \(P = 14\) into the equation: \(14=6 + 2t\).

Step3: Solve for \(t\)

Subtract 6 from both sides: \(14-6=2t\), which gives \(8 = 2t\). Then divide both sides by 2: \(t=\frac{8}{2}\).

Answer:

\(4\)