Question

triangle fgh is similar to triangle ijk. find the measure of side jk. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Set up proportion

Since $\triangle FGH\sim\triangle IJK$, the ratios of corresponding - sides are equal. Let $JK = x$. We have the proportion $\frac{FG}{IJ}=\frac{GH}{JK}$. Here, $FG = 11$, $IJ = 46$, and $GH = 16$. So the proportion is $\frac{11}{46}=\frac{16}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $11x=46\times16$.

Step3: Calculate the right - hand side

$46\times16 = 736$, so $11x = 736$.

Step4: Solve for x

$x=\frac{736}{11}\approx66.9$.

Answer:

$66.9$