Question

If angle I is congruent to angle K find the perimeter of triangle JIK?

Answer 1

The perimeter of a triangle is given by the sum its three sides, then according to the figure above we have that:

$P=(7x-5)+(6x-5)+(9x-11) \\ \\ \therefore P=22x-21$

Thus, our goal is to find the value of $x$ and by finding it we will get the perimeter of the triangle. If ∠I = ∠K = β, then according to the Law of Sines we have:

$\frac{9x-11}{sin \beta}= \frac{6x-5}{sin \beta} \\ \\ \therefore 9x-11=6x-5 \\ \therefore 3x=6 \therefore \boxed{x=2}$

Lastly, the perimeter is:

$P=22(2)-21 \rightarrow \boxed{P=23 \ units}$