Question

A surveyor is measuring the distance across a canyon. He sets up two similar right triangles and finds that the length of CD = 12 feet and the length of DE = 16 feet.

If △ABC ~ △EDC, what is the length side AB?

Answer 1

The length side AB is 64 ft , Option D is the correct answer.

What is a Right triangle ?

A triangle that has one angle 90 degree is called Right angled Triangle.

From the figure it can be seen that

The triangle CDE is a right Triangle

Applying Pythagoras theorem to find the length of CE

CE² = 12² + 16²

CE = 20 ft

As both the triangles are similar therefore the ratio of the sides will be equal

BC : CD = AC : CE

48 / 12 = AC / 20

AC = 80ft

As Triangle ABC is also a right angled triangle

Applying Pythagoras theorem to find the length of AB

AC² = BC² +AB²

6400 = 48² +AB²

AB² = 4096

AB = 64 ft

Therefore Option D is the correct answer.

To know more about Right Triangle

https://brainly.com/question/6322314

#SPJ1