Find the value of x assume the triangles are the same

Question

asked Dec 18, 2023 213k views

1 Answer

Jaga · Answer 1 · 2023-12-22T04:01:18+0000

1) In this problem, we need to find the constant of proportionality assuming these triangles are similar. So let's divide each corresponding leg:

$(22)/(18)=(33)/(27)\Rightarrow\:k=(11)/(9)$

2) So, based on that constant of proportionality (k) we can find the missing leg.

$\begin{gathered} x/(11)/(9)=36 \\ \\ x\cdot(9)/(11)=36 \\ \\ 11*(9)/(11)x=36*11 \\ \\ 9x=396 \\ \\ (9x)/(9)=(396)/(9) \\ \\ x=44 \end{gathered}$

Note that since the triangle on the top is larger than the one on the bottom, we can tell that x must be larger than 36.