Meeru had lost her way home and was standing 25 meters away from her house in the southwest direction. She walks 20 meters north and reaches point A. How far and in which direction would she have to walk to reach her house?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

She has to walk 15 meters in the East direction to reach her house. Steps to calculate how far and in which direction would she have to walk to reach her house:

Step 1: Create a basic diagram using the information provided.

a right-angled triangle ABC is created, with hypotenuses AB and AC measuring 25 meters and 20 meters, respectively

Here, a right-angled triangle ABC is created, with hypotenuses AB and AC measuring 25 meters and 20 meters, respectively.

She must therefore go a CB distance in an easterly direction to get to her dwelling.

Table of content

1. Meeru had lost her way home and was standing 25 meters away from her house in the southwest direction. She walks 20 meters north and reaches point A. How far and in which direction would she have to walk to reach her house?

Step 2: To determine the length of AB, use the Pythagorean theorem.

According to Pythagoras’ theorem, the square of the hypotenuse in a right triangle equals the sum of the squares of the other two sides.

CB2 + CA2 = AB2

Substituting the values we get:

CB2 + 202 = 252

CB2 + 400 = 625

CB2 = 625 – 400

Taking square root:

CB = √225

CB = 15 meter

She must therefore travel 15 meters east to get to her home.

Applications of Pythagoras theorem

to determine whether or not the triangle is right-angled.
If the other two sides of a right-angled triangle are known, we can determine the length of any side.
to establish the square’s diagonal.

Summary: