Question

Triangles FIM and LAK below are similar, and LA=AKWhat is the length of LA?

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define similar triangles

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

STEP 2: Express their corresponding sides as a ratio that will be equal

Since, the given triangles are equal, therefore the ratios of their corresponding sides are equal. That is;

`(FI)/(LA)=(FM)/(LK)=(IM)/(AK)`

STEP 3: Substitute the lenghts of the given sides.

`\begin{gathered} FI=6,IM=6,FM=8,LK=12 \\ By\text{ substitution,} \\ (6)/(LA)=(8)/(12)=(6)/(AK) \end{gathered}`

STEP 4: Solve for LA

`\begin{gathered} (6)/(LA)=(8)/(12) \\ By\text{ cross multiplication,} \\ 6*12=8* LA \\ 72=8* LA \\ LA=(72)/(8)=9 \end{gathered}`

Hence, the length of LA is 9