Question

1. the following two right triangles are similar.if side de = 45, side hi = 36, and side df = 30, what is the length of side hj? 21 19 24 20

Explanation:

Step1: Set up proportion for similar - triangles

For similar right - triangles, the ratios of corresponding sides are equal. Let $\triangle DEF\sim\triangle HIJ$. Then $\frac{DE}{HI}=\frac{DF}{HJ}$.

Step2: Substitute given values

We know that $DE = 45$, $HI = 36$, and $DF = 30$. Substituting these values into the proportion $\frac{45}{36}=\frac{30}{HJ}$.

Step3: Cross - multiply

Cross - multiplying gives us $45\times HJ=36\times30$.

Step4: Solve for $HJ$

First, calculate $36\times30 = 1080$. Then $HJ=\frac{1080}{45}=24$.

Answer:

24