A surveyor is measuring the distance across a canyon. He sets up two similar right triangles and finds that the length of CD = 1

Question

2 years ago

13

2 feet and the length of DE = 16 feet.
If △ABC ~ △EDC, what is the length side AB?

1 answer:

Citrus2011 [14] · Answer 1 · 2023-06-05T09:08:55+03:00

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

<h3>What is a Right triangle ?</h3>

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

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