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balu736 [363]
3 years ago
11

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

Mathematics
1 answer:
inessss [21]3 years ago
3 0
The perimeter of a triangle is given by <em>the sum its three sides</em>, 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}

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