Question

the triangles are similar. solve for x. (hint: use the similarity statement to set up the equation as a proportion). 4 + 10x 30 h n k 90 70 m t △mhd~△nkt

Explanation:

Step1: Set up proportion

Since $\triangle MHD\sim\triangle NKT$, the ratios of corresponding sides are equal. So, $\frac{4 + 10x}{30}=\frac{90}{70}$.

Step2: Cross - multiply

Cross - multiplying gives $70(4 + 10x)=30\times90$.
Expanding the left - hand side: $280+700x = 2700$.

Step3: Isolate the variable term

Subtract 280 from both sides: $700x=2700 - 280$.
$700x=2420$.

Step4: Solve for x

Divide both sides by 700: $x=\frac{2420}{700}=\frac{121}{35}\approx3.46$.

Answer:

$x = \frac{121}{35}$