Question

Which value of x proves that the two triangles above are similar? 42.7 ft 26.7 ft 10 ft 25.6 ft

Answer 1

`x=26.7\text{ ft}`

Step-by-step explanation

Step 1

we have two triangles

ACE and BCD

if the triangles are similar, then the ratio of the sides must be the same:

`\begin{gathered} \frac{\text{red line}}{purple\text{ line}}=\frac{blue\text{ line}}{\text{green line}} \\ \text{replacing} \\ (16+x)/(32)=(x)/(20) \end{gathered}`

Step 2

solve for x

`\begin{gathered} (16+x)/(32)=(x)/(20) \\ \text{cross multiply} \\ 20(16+x)=32\cdot x \\ 320+20x=32x \\ \text{subtrac 20x in both sides} \\ 320+20x-20x=32x-20x \\ 320=12x \\ \text{divide both sides y 12} \\ (320)/(12)=(12x)/(12) \\ \text{ x=26.66} \end{gathered}`

rounded

`x=26.7\text{ }`

I hope this helps you